© Oxford University
Academic Lectures from University of Oxford's Department of Physics.
The video series for this podcast includes content previously published in 2016 as 'Reduced Density Matrices in Quantum Physics and Role of Fermionic Exchange Symmetry': "The interdisciplinary workshop brings together experts in quantum science, as e.g. quantum information theory, quantum chemistry, solid state physics and mathematical physics. The aim is to explore from a conceptual viewpoint the influence of the fermionic exchange symmetry and its consequences for the reduced 1and 2fermion picture. In particular, a better understanding should be developed of how the conflict of energy minimization and antisymmetry of the Nfermion quantum state leads to simplified descriptions of fermionic ground states."
en
Thu, 28 Mar 2019 11:40:20 +0000
http://www.physics.ox.ac.uk/confs/pauli2016/index.asp
Oxford Physics Academic Lectures
Oxford University
Oxford University
podcasts@it.ox.ac.uk
no
http://mediapub.it.ox.ac.uk/sites/fred/files/default_images/defaultradcliffe.jpg
Oxford Physics Academic Lectures
http://www.physics.ox.ac.uk/confs/pauli2016/index.asp

1
quantum
matrices
chemistry
In my talk I will attempt to provide an overview on the application of the density matrix renormalization group (DMRG) algorithm in quantum chemistry. I will compare to traditional approaches with respect to limitations and capabilities. I will highlight the ma trix product operator structure of our secondgeneration DMRG program and discuss its features. Emphasis will be put on how orbitalentanglement measures can be exploited to automatically select proper active orbital spaces, a major problem of all multiconfigurational approaches.
http://rss.oucs.ox.ac.uk/tag:20190328:114020:000:file:306880:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420_markus_reiher_friday.mp4
In my talk I will attempt to provide an overview on the application of the density matrix renormalization group (DMRG) algorithm in quantum chemistry.
In my talk I will attempt to provide an overview on the application of the density matrix renormalization group (DMRG) algorithm in quantum chemistry. I will compare to traditional approaches with respect to limitations and capabilities. I will highlight the ma trix product operator structure of our secondgeneration DMRG program and discuss its features. Emphasis will be put on how orbitalentanglement measures can be exploited to automatically select proper active orbital spaces, a major problem of all multiconfigurational approaches.
quantum,matrices,chemistry
Markus Reiher
4033
Tue, 11 Oct 2016 00:00:17 +0100

2
matrices
quantum
systems
In this talk, I will introduce DMRG both from the historical (statistical) and modern (matrix product state) perspective, highlighting why it has become the method of choice for onedimensional quantum systems in and out of equilibrium. I will talk as well as why it has made interesting forays into the world of twodimensional quantum systems. I will also discuss its limitations, as well as the resulting directions of future development.
http://rss.oucs.ox.ac.uk/tag:20190328:113817:000:file:306879:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420_ulrich_schollwock_friday.mp4
In this talk, I will introduce DMRG both from the historical (statistical) and modern (matrix product state) perspective, highlighting why it has become the method of choice for onedimensional quantum systems in and out of equilibrium.
In this talk, I will introduce DMRG both from the historical (statistical) and modern (matrix product state) perspective, highlighting why it has become the method of choice for onedimensional quantum systems in and out of equilibrium. I will talk as well as why it has made interesting forays into the world of twodimensional quantum systems. I will also discuss its limitations, as well as the resulting directions of future development.
matrices,quantum,systems
Ulrich Schollwöck
4869
Tue, 11 Oct 2016 00:00:16 +0100

3
quantum
fermionic
matrices
Information about the interaction of a manyelectron quantum system with its environment is encoded within the oneelectron density matrix (1RDM). While the 1RDM from an ensemble manyelectron quantum system must obey the Pauli exclusion principle, the 1RDM from a pure quantum system must obey additional constraints known as the generalized Pauli conditions. By examining the 1RDM’s violation of these generalized Pauli conditions, we obtain a sufficient condition at the level of a single electron for a manyelectron quantum system’s openness. As the system interacts with the environment, the more stringent generalized Pauli conditions relax to the Pauli principle, the nature and extent of this relaxation serving to quantify the degree openness of a manyelectron quantum system. In an application to photosynthetic light harvesting we show that the interaction of the system with the environment (quantum noise) relaxes significant constraints imposed on the exciton dynamics by the generalized Pauli conditions. This relaxation provides a geometric (kinematic) interpretation for the role of noise in enhancing exciton transport in quantum systems.
http://rss.oucs.ox.ac.uk/tag:20190328:113429:000:file:306878:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420_romit_chakraborty_thursday.mp4
Information about the interaction of a manyelectron quantum system with its environment is encoded within the oneelectron density matrix (1RDM).
Information about the interaction of a manyelectron quantum system with its environment is encoded within the oneelectron density matrix (1RDM). While the 1RDM from an ensemble manyelectron quantum system must obey the Pauli exclusion principle, the 1RDM from a pure quantum system must obey additional constraints known as the generalized Pauli conditions. By examining the 1RDM’s violation of these generalized Pauli conditions, we obtain a sufficient condition at the level of a single electron for a manyelectron quantum system’s openness. As the system interacts with the environment, the more stringent generalized Pauli conditions relax to the Pauli principle, the nature and extent of this relaxation serving to quantify the degree openness of a manyelectron quantum system. In an application to photosynthetic light harvesting we show that the interaction of the system with the environment (quantum noise) relaxes significant constraints imposed on the exciton dynamics by the generalized Pauli conditions. This relaxation provides a geometric (kinematic) interpretation for the role of noise in enhancing exciton transport in quantum systems.
quantum,fermionic,matrices
Romit Chakraborty
1279
Tue, 11 Oct 2016 00:00:15 +0100

4
electron
Energy
matrices
Reduced Density Matrix Functional Theory is a method that relies on the 11 correspondence between the ground state wavefunction of many electron systems and the first order reduced density matrix(1RDM) and uses the second one as its fundamental valuable. The ground state of a system is determined within this approach by minimizing the energy functional with respect to the 1RDM while satisfying that the 1RDM corresponds to a fermionic ensemble (Coleman’s conditions). As the explicit expression of the energy functional with respect to the 1RDM is not known, different approximate functionals are employed. If we had the exact functional performing the energy minimization using the ensemble representability constraints would be enough to find a 1RDM that corresponds to a pure state (if our ground state is not degenerate so we really have a pure state). However, performing the energy minimization with approximate functionals, as we found for 3 electron systems test cases, results in occupation numbers that do not satisfy the generalized Pauli constraints (GPC). One then could in principle employ the GPC as additional constraints during the energy minimization to ensure that the ground state 1RDM that finds can result from a pure state. However due to the big number of these constraints this is not feasible in practice apart from a few cases of really small systems.
An idea to be explored is constructing energy functionals that satisfy at least some of the GPC. This could serve as a change of paradigm for functional derivation because until now 1RDM functionals were mostly tested on whether they reproduced or not ground state energies correctly. Another idea that we would like to discuss is whether we could apply the GPC in an approximate way to only the electrons that have occupations smaller than one. The electrons with occupation one do not play any role to whether the 1RDM corresponds to a pure state or not. Although it is doubtful whether 1RDMs with occupations that are exactly one can correspond to a ground state of a real fermionic system, in many cases this is a sensible approximation that would significantly reduce the amount of GPC to be considered in a RDMFT minimization.
http://rss.oucs.ox.ac.uk/tag:20190328:113030:000:file:306877:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420_iris_theophilou_thursday.mp4
Reduced Density Matrix Functional Theory is a method that relies on the 11 correspondence between the ground state wavefunction of many electron systems and the first order reduced density matrix(1RDM) and uses the second one as its fundamental valuable.
Reduced Density Matrix Functional Theory is a method that relies on the 11 correspondence between the ground state wavefunction of many electron systems and the first order reduced density matrix(1RDM) and uses the second one as its fundamental valuable. The ground state of a system is determined within this approach by minimizing the energy functional with respect to the 1RDM while satisfying that the 1RDM corresponds to a fermionic ensemble (Coleman’s conditions). As the explicit expression of the energy functional with respect to the 1RDM is not known, different approximate functionals are employed. If we had the exact functional performing the energy minimization using the ensemble representability constraints would be enough to find a 1RDM that corresponds to a pure state (if our ground state is not degenerate so we really have a pure state). However, performing the energy minimization with approximate functionals, as we found for 3 electron systems test cases, results in occupation numbers that do not satisfy the generalized Pauli constraints (GPC). One then could in principle employ the GPC as additional constraints during the energy minimization to ensure that the ground state 1RDM that finds can result from a pure state. However due to the big number of these constraints this is not feasible in practice apart from a few cases of really small systems.
An idea to be explored is constructing energy functionals that satisfy at least some of the GPC. This could serve as a change of paradigm for functional derivation because until now 1RDM functionals were mostly tested on whether they reproduced or not ground state energies correctly. Another idea that we would like to discuss is whether we could apply the GPC in an approximate way to only the electrons that have occupations smaller than one. The electrons with occupation one do not play any role to whether the 1RDM corresponds to a pure state or not. Although it is doubtful whether 1RDMs with occupations that are exactly one can correspond to a ground state of a real fermionic system, in many cases this is a sensible approximation that would significantly reduce the amount of GPC to be considered in a RDMFT minimization.
electron,Energy,matrices
Iris Theophilou
1964
Tue, 11 Oct 2016 00:00:14 +0100

5
electrons
fermionic
numbers
It is now known that fermionic natural occupation numbers (NON) do not only obey Pauli’s exclusion principle but are even stronger restricted by the socalled generalized Pauli constraints (GPC). So far, the nature of these constraints has been explored in some systems: a model of few spinless fermions confined to a onedimensional harmonic potential, the lithium isoelectronic series and ground and excited states of some three, four and fiveelectron atomic and molecular systems. Whenever given NON lie on the boundary of the allowed region the corresponding Nfermion quantum state has a significantly simpler structure. By employing this structure a variational optimization method for few fermion ground states is elaborated. We quantitatively confirm its high accuracy for systems with the vector of NON in a small distance to the boundary of the polytope. In particular, we derive an upper bound on the error of the correlation energy given by the ratio of the distance to the boundary of the polytope and the distance of the vector of NON to the HartreeFock point. Moreover, these geometric insights shed some light on the concept of active spaces, correlation energy, frozen electrons and virtual orbitals.
http://rss.oucs.ox.ac.uk/tag:20190328:112621:000:file:306876:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420_carlos_benavidesriveros_thursday.mp4
It is now known that fermionic natural occupation numbers (NON) do not only obey Pauli’s exclusion principle but are even stronger restricted by the socalled generalized Pauli constraints (GPC).
It is now known that fermionic natural occupation numbers (NON) do not only obey Pauli’s exclusion principle but are even stronger restricted by the socalled generalized Pauli constraints (GPC). So far, the nature of these constraints has been explored in some systems: a model of few spinless fermions confined to a onedimensional harmonic potential, the lithium isoelectronic series and ground and excited states of some three, four and fiveelectron atomic and molecular systems. Whenever given NON lie on the boundary of the allowed region the corresponding Nfermion quantum state has a significantly simpler structure. By employing this structure a variational optimization method for few fermion ground states is elaborated. We quantitatively confirm its high accuracy for systems with the vector of NON in a small distance to the boundary of the polytope. In particular, we derive an upper bound on the error of the correlation energy given by the ratio of the distance to the boundary of the polytope and the distance of the vector of NON to the HartreeFock point. Moreover, these geometric insights shed some light on the concept of active spaces, correlation energy, frozen electrons and virtual orbitals.
electrons,fermionic,numbers
Carlos BenavidesRiveros
3122
Tue, 11 Oct 2016 00:00:13 +0100

6
quantum
fermionic
symmetry
The Pauli exclusion principle has a strong impact on the properties and the behavior of most fermionic quantum systems. Remarkably, even stronger restrictions on fermionic natural occupation numbers follow from the fermionic exchange symmetry. We develop an operationally meaningful measure which allows one to quantify the potential physical relevance of those generalized Pauli constraints beyond the wellestablished relevance of Pauli’s exclusion principle. It is based on a geometric hierarchy induced by Pauli exclusion principle constraints. The significance of that measure is illustrated for a fewfermion model which also confirms such nontrivial relevance of the generalized Pauli constraints.
http://rss.oucs.ox.ac.uk/tag:20190328:112356:000:file:306875:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420_felix_tennie_thursday.mp4
The Pauli exclusion principle has a strong impact on the properties and the behavior of most fermionic quantum systems. Remarkably, even stronger restrictions on fermionic natural occupation numbers follow from the fermionic exchange symmetry.
The Pauli exclusion principle has a strong impact on the properties and the behavior of most fermionic quantum systems. Remarkably, even stronger restrictions on fermionic natural occupation numbers follow from the fermionic exchange symmetry. We develop an operationally meaningful measure which allows one to quantify the potential physical relevance of those generalized Pauli constraints beyond the wellestablished relevance of Pauli’s exclusion principle. It is based on a geometric hierarchy induced by Pauli exclusion principle constraints. The significance of that measure is illustrated for a fewfermion model which also confirms such nontrivial relevance of the generalized Pauli constraints.
quantum,fermionic,symmetry
Felix Tennie
3587
Tue, 11 Oct 2016 00:00:12 +0100

7
fermionic
pauli exclusion
The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected since at least the 1970’s, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Here, we provide the first analytic analysis of the physical relevance of these constraints. We compute the natural occupation numbers for the ground states of a family of interacting fermions in a harmonic potential. Intriguingly, we find that the occupation numbers are almost, but not exactly, pinned to the boundary of the allowed region (quasipinned). The result suggests that the physics behind the phenomenon is richer than previously appreciated. In particular, it shows that for some models, the generalized Pauli constraints play a role for the ground state, even though they do not limit the groundstate energy. Our findings suggest a generalization of the HartreeFock approximation.
http://rss.oucs.ox.ac.uk/tag:20190328:112125:000:file:306874:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420_mathhias_christandl_thursday.mp4
The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states.
The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected since at least the 1970’s, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Here, we provide the first analytic analysis of the physical relevance of these constraints. We compute the natural occupation numbers for the ground states of a family of interacting fermions in a harmonic potential. Intriguingly, we find that the occupation numbers are almost, but not exactly, pinned to the boundary of the allowed region (quasipinned). The result suggests that the physics behind the phenomenon is richer than previously appreciated. In particular, it shows that for some models, the generalized Pauli constraints play a role for the ground state, even though they do not limit the groundstate energy. Our findings suggest a generalization of the HartreeFock approximation.
fermionic,pauli exclusion
Matthias Christandl
3357
Tue, 11 Oct 2016 00:00:11 +0100

8
fermionic
algorithm
In the talk I am planning to explain two different solutions of Nrepresentability problem and then give the algorithm to calculate GPCs. After that, as examples I will show my calculations for 3 fermions systems of rank 6 and 7 for which the algorithm works smoothly. For higher rank systems we need an additional tool which I will try to explain also.
http://rss.oucs.ox.ac.uk/tag:20190328:111841:000:file:306873:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420_murat_altunbulak_thursday.mp4
In the talk I am planning to explain two different solutions of Nrepresentability problem and then give the algorithm to calculate GPCs.
In the talk I am planning to explain two different solutions of Nrepresentability problem and then give the algorithm to calculate GPCs. After that, as examples I will show my calculations for 3 fermions systems of rank 6 and 7 for which the algorithm works smoothly. For higher rank systems we need an additional tool which I will try to explain also.
fermionic,algorithm
Murat Altunbulak
1565
Tue, 11 Oct 2016 00:00:10 +0100

9
sermonic
microscopic
numerical analysis
In the talk I will present recent progress in proving closeness of the microscopic and effective description for systems of many fermions. Solving the time dependent Schrödinger equation for a system of many interacting Fermions is in many cases impossible, both analytically and numerically. Instead of the microscopic description one uses an effective description which describes the behaviour of the fermions in good approximation and can be treated with a computer. In many cases one uses the fermionic Hartree or HartreeFock equation as effective description.
http://rss.oucs.ox.ac.uk/tag:20190328:111511:000:file:306872:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420_peter_pickl_wednesday.mp4
In the talk I will present recent progress in proving closeness of the microscopic and effective description for systems of many fermions.
In the talk I will present recent progress in proving closeness of the microscopic and effective description for systems of many fermions. Solving the time dependent Schrödinger equation for a system of many interacting Fermions is in many cases impossible, both analytically and numerically. Instead of the microscopic description one uses an effective description which describes the behaviour of the fermions in good approximation and can be treated with a computer. In many cases one uses the fermionic Hartree or HartreeFock equation as effective description.
sermonic,microscopic,numerical analysis
Peter Pickl
3773
Tue, 11 Oct 2016 00:00:09 +0100

10
orbitals
matrices
Physical Meaning of Natural Orbitals and Natural Occupation Numbers By their definition, the natural orbitals and occupation numbers are the eigenfunctions and eigenvalues of the onebody reduced density matrix. This raises the question to which extend one can assign a physical interpretation to them, e.g. if the degeneracies in the occupation numbers reflect the symmetries of the system or if an excitation can be described by simply changing the occupations of the groundstate natural orbitals. We use exactly solvable model systems to investigate the suitability of natural orbitals as a basis for describing manybody excitations. We analyze to which extend the natural orbitals describe both bound as well as ionized excited states and show that depending on the specifics of the excited state the groundstate natural orbitals yield a good approximation or not.
http://rss.oucs.ox.ac.uk/tag:20190328:111450:000:file:306871:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420_n_helbig_wednesday.mp4
Physical Meaning of Natural Orbitals and Natural Occupation Numbers
Physical Meaning of Natural Orbitals and Natural Occupation Numbers By their definition, the natural orbitals and occupation numbers are the eigenfunctions and eigenvalues of the onebody reduced density matrix. This raises the question to which extend one can assign a physical interpretation to them, e.g. if the degeneracies in the occupation numbers reflect the symmetries of the system or if an excitation can be described by simply changing the occupations of the groundstate natural orbitals. We use exactly solvable model systems to investigate the suitability of natural orbitals as a basis for describing manybody excitations. We analyze to which extend the natural orbitals describe both bound as well as ionized excited states and show that depending on the specifics of the excited state the groundstate natural orbitals yield a good approximation or not.
orbitals,matrices
Nicole Helbig
2361
Tue, 11 Oct 2016 00:00:08 +0100

11
functional theory
fermionic
quantum
In this presentation, we review the theoretical foundations of RDMFT the most successful approximations and extensions, we assess presentday functionals on applications to molecular and periodic systems and we discuss the challenges and future prospect Reduced density matrix functional theory (RDMFT) is a theoretical framework for approximating the manyelectron problem. In RDMFT, the fundamental quantity is the onebody, reduced, density matrix (1RDM) which plays the same role as the electronic density in density functional theory. Gilberts theorem stands in the foundations of RMDFT, and guarantees that every observable for the ground state is a functional of the 1RDM. This allows for approximating the total energy in terms of the 1RDM and minimizing it under certain conditions for the Nrepresentability of the 1RDM. So far, in almost all practical applications Coleman’s ensemble Nrepresentability conditions are employed which are very simple for fermionic systems. They concern the eigenvalues of the 1RDM, known as natural occupations, restricting then in the range between zero and one and their sum which is fixed to be the total number of electrons.
A certain advantage of tackling the many electron problem in this way is that the kinetic energy of the system is a simple expression in terms of the 1RDM, i.e. there is no need for a fictitious non interacting system like the KohnSham system in DFT. Thus, fractional occupations enter the theory in a natural way allowing to construct simple approximations that describe accurately electronic correlations. A central and simple functional in RDMFT is the Mler functional, a relatively simple modification of the expression of the total energy in HartreeFock theory. This functional was shown to reproduce the correct physical picture of the dissociation of the Hydrogen molecule, although it is known to overestimate substantially the correlation energy. Several approximations were introduced in the last couple of decades, many of which are corrections to the Mller functional, and were proven to describe accurately such diverse effects and quantities like static correlations and the band gaps of materials. Unfortunately, due to the nonexistence of a noninteracting systems, RDMFT calculations are demanding compared to DFT and, at present, are restricted to small molecules or simple periodic systems.
http://rss.oucs.ox.ac.uk/tag:20190328:110515:000:file:306870:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420_n_lathiotakis_wednesday.mp4
In this presentation, we review the theoretical foundations of RDMFT the most successful approximations and extensions, we assess presentday functionals on applications to molecular and periodic systems and we discuss the challenges and future prospect
In this presentation, we review the theoretical foundations of RDMFT the most successful approximations and extensions, we assess presentday functionals on applications to molecular and periodic systems and we discuss the challenges and future prospect Reduced density matrix functional theory (RDMFT) is a theoretical framework for approximating the manyelectron problem. In RDMFT, the fundamental quantity is the onebody, reduced, density matrix (1RDM) which plays the same role as the electronic density in density functional theory. Gilberts theorem stands in the foundations of RMDFT, and guarantees that every observable for the ground state is a functional of the 1RDM. This allows for approximating the total energy in terms of the 1RDM and minimizing it under certain conditions for the Nrepresentability of the 1RDM. So far, in almost all practical applications Coleman’s ensemble Nrepresentability conditions are employed which are very simple for fermionic systems. They concern the eigenvalues of the 1RDM, known as natural occupations, restricting then in the range between zero and one and their sum which is fixed to be the total number of electrons.
A certain advantage of tackling the many electron problem in this way is that the kinetic energy of the system is a simple expression in terms of the 1RDM, i.e. there is no need for a fictitious non interacting system like the KohnSham system in DFT. Thus, fractional occupations enter the theory in a natural way allowing to construct simple approximations that describe accurately electronic correlations. A central and simple functional in RDMFT is the Mler functional, a relatively simple modification of the expression of the total energy in HartreeFock theory. This functional was shown to reproduce the correct physical picture of the dissociation of the Hydrogen molecule, although it is known to overestimate substantially the correlation energy. Several approximations were introduced in the last couple of decades, many of which are corrections to the Mller functional, and were proven to describe accurately such diverse effects and quantities like static correlations and the band gaps of materials. Unfortunately, due to the nonexistence of a noninteracting systems, RDMFT calculations are demanding compared to DFT and, at present, are restricted to small molecules or simple periodic systems.
functional theory,fermionic,quantum
Nektarios N. Lathiotakis
3477
Tue, 11 Oct 2016 00:00:07 +0100

12
complexity
quantum
mathematics
I will give an introduction to the univariate quantum marginal problem using an elementary mathematical point of view. In particular, I will explain how extremality of the local spectrum carries structural information about the global wave function. The talk will also give some quantum information background, touching e.g. on the computational complexity of general quantum marginal problems and relations to entanglement.
http://rss.oucs.ox.ac.uk/tag:20190328:110254:000:file:306869:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420_david_gross_wednesday.mp4
I will give an introduction to the univariate quantum marginal problem using an elementary mathematical point of view. In particular, I will explain how extremality of the local spectrum carries structural information about the global wave function.
I will give an introduction to the univariate quantum marginal problem using an elementary mathematical point of view. In particular, I will explain how extremality of the local spectrum carries structural information about the global wave function. The talk will also give some quantum information background, touching e.g. on the computational complexity of general quantum marginal problems and relations to entanglement.
complexity,quantum,mathematics
David Gross
3542
Tue, 11 Oct 2016 00:00:06 +0100

13
matches
correlation
electron
quantum
Strongly correlated quantum systems are not easily described with conventional quantum chemistry formalism because the number of nonnegligible configurations grows exponen tially with the number of orbitals actively participating in the correlation. In this lecture we will introduce the concept of reduced density matrices for systems of identical fermions and comment on their relevance to problems in quantum chemistry and physics, especially the description of strongly correlated quantum systems. We will discuss Coulsons challenge in which Coulson highlighted the potential advantages of a direct calculation of the twoelectron reduced density matrix without the manyelectron wave function and cautioned against the difficulty of ensuring that the twoelectron reduced density matrix represents an Nelectron quantum system, known as the Nrepresentability problem. We will present recent advances for the direct calculation of the twoelectron reduced density matrix including the implementation of Nrepresentability conditions by semidefinite programming. Twoelectron reduced density matrix (2RDM) methods can accurately approximate strong electron correlation in molecules and materials at a computational cost that grows nonexponentially with system size [5]. In an application we will treat a quantum chemical system with sextillion (1021) quantum degrees of freedom to reveal the important role of quantum entanglement in its oxidation and reduction.
http://rss.oucs.ox.ac.uk/tag:20190328:105658:000:file:306868:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420_david_mazziotti_wednesday.mp4
Strongly correlated quantum systems are not easily described with conventional quantum chemistry formalism because the number of nonnegligible configurations grows exponen tially with the number of orbitals actively participating in the correlation.
Strongly correlated quantum systems are not easily described with conventional quantum chemistry formalism because the number of nonnegligible configurations grows exponen tially with the number of orbitals actively participating in the correlation. In this lecture we will introduce the concept of reduced density matrices for systems of identical fermions and comment on their relevance to problems in quantum chemistry and physics, especially the description of strongly correlated quantum systems. We will discuss Coulsons challenge in which Coulson highlighted the potential advantages of a direct calculation of the twoelectron reduced density matrix without the manyelectron wave function and cautioned against the difficulty of ensuring that the twoelectron reduced density matrix represents an Nelectron quantum system, known as the Nrepresentability problem. We will present recent advances for the direct calculation of the twoelectron reduced density matrix including the implementation of Nrepresentability conditions by semidefinite programming. Twoelectron reduced density matrix (2RDM) methods can accurately approximate strong electron correlation in molecules and materials at a computational cost that grows nonexponentially with system size [5]. In an application we will treat a quantum chemical system with sextillion (1021) quantum degrees of freedom to reveal the important role of quantum entanglement in its oxidation and reduction.
matches,correlation,electron,quantum
David A. Mazziotti
3550
Tue, 11 Oct 2016 00:00:05 +0100

14
quantum
entanglement
matrices
In this talk, we will give an overview of the entanglement spectroscopy with a focus on to the fractional quantum Hall phases. We will show how much information is encoded within the ground state and how different partitions probe different types of excitations. The entanglement spectroscopy, initially introduced by Li and Haldane in the context of the fractional quantum Hall effects, has stimulated an extensive range of studies. The entanglement spectrum is the spectrum of the reduced density matrix, when we partition the system into two. For many quantum systems, it unveils a unique feature: Computed from the bulk ground state wave function, the entanglement spectrum give access to the physics of edge excitations.
http://rss.oucs.ox.ac.uk/tag:20190327:170156:000:file:306862:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420_nicolas_regnault_tuesday.mp4
In this talk, we will give an overview of the entanglement spectroscopy with a focus on to the fractional quantum Hall phases.
In this talk, we will give an overview of the entanglement spectroscopy with a focus on to the fractional quantum Hall phases. We will show how much information is encoded within the ground state and how different partitions probe different types of excitations. The entanglement spectroscopy, initially introduced by Li and Haldane in the context of the fractional quantum Hall effects, has stimulated an extensive range of studies. The entanglement spectrum is the spectrum of the reduced density matrix, when we partition the system into two. For many quantum systems, it unveils a unique feature: Computed from the bulk ground state wave function, the entanglement spectrum give access to the physics of edge excitations.
quantum,entanglement,matrices
Nicolas Regnault
3092
Tue, 11 Oct 2016 00:00:04 +0100

15
quantum
errors
knots
particles
anyon
In this talk Jiannis Pachos discusses a variety of different topics starting from characterizing knot invariants, their quantum simulation with exotic particles called anyons and finally the possible realization of anyons in the laboratory. Combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding field of research focused on the exploration of quantum evolutions that are resilient to errors.
http://rss.oucs.ox.ac.uk/tag:20190327:165943:000:file:306861:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420jiannis_pachos_Tuesday.mp4
In this talk Jiannis Pachos discusses a variety of different topics starting from characterizing knot invariants, their quantum simulation with exotic particles called anyons and finally the possible realization of anyons in the laboratory.
In this talk Jiannis Pachos discusses a variety of different topics starting from characterizing knot invariants, their quantum simulation with exotic particles called anyons and finally the possible realization of anyons in the laboratory. Combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding field of research focused on the exploration of quantum evolutions that are resilient to errors.
quantum,errors,knots,particles,anyon
Jiannis Pachos
3312
Tue, 11 Oct 2016 00:00:03 +0100

16
quantum
anyon
statistics
Duncan Haldane talks about Quantum Geometry, Exclusion Statistics, and the Geometry of "Flux Attachment" in 2D Landau levels. The degenerate partiallyfilled 2D Landau level is a remarkable environment in which kinetic energy is replaced by "quantum geometry" (or an uncertainty principle) that quantises the space occupied by the electrons quite differently from the atomicscale quantisation by a periodic arrangement of atoms. In this arena, when the shortrange part of the Coulomb interaction dominates, it can lead to "flux attachment", where a particle (or cluster of particles) exclusively occupies a quantised region of space. This principle underlies both the incompressible fractional quantum Hall fluids an the composite fermion Fermi liquid states that occur in such systems.
http://rss.oucs.ox.ac.uk/tag:20190327:165741:000:file:306860:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420duncan_haldane_tuesday.mp4
Duncan Haldane talks about Quantum Geometry, Exclusion Statistics, and the Geometry of "Flux Attachment" in 2D Landau levels.
Duncan Haldane talks about Quantum Geometry, Exclusion Statistics, and the Geometry of "Flux Attachment" in 2D Landau levels. The degenerate partiallyfilled 2D Landau level is a remarkable environment in which kinetic energy is replaced by "quantum geometry" (or an uncertainty principle) that quantises the space occupied by the electrons quite differently from the atomicscale quantisation by a periodic arrangement of atoms. In this arena, when the shortrange part of the Coulomb interaction dominates, it can lead to "flux attachment", where a particle (or cluster of particles) exclusively occupies a quantised region of space. This principle underlies both the incompressible fractional quantum Hall fluids an the composite fermion Fermi liquid states that occur in such systems.
quantum,anyon,statistics
Duncan Haldane
4613
Tue, 11 Oct 2016 00:00:02 +0100

17
anyon
exclusion
neutrons
quantum
This talk mentions some aspects of the theory of identical particles, for example, treating neutrons and protons as identical particles distinguished by a quantum number called isotopic spin. He will also review studies of systems of three or more anyons. In particular, the virial expansion shows that the free anyon gas approximates exclusion statistics, with a correspondence between the anyon parameter and the exclusion parameter which is different from the case of anyons in a magnetic field, discussed in the talk by Jon Magne Leinaas.
http://rss.oucs.ox.ac.uk/tag:20190327:165514:000:file:306859:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420jan_myrheim_Tuesday.mp4
This talk mentions some aspects of the theory of identical particles, for example, treating neutrons and protons as identical particles distinguished by a quantum number called isotopic spin.
This talk mentions some aspects of the theory of identical particles, for example, treating neutrons and protons as identical particles distinguished by a quantum number called isotopic spin. He will also review studies of systems of three or more anyons. In particular, the virial expansion shows that the free anyon gas approximates exclusion statistics, with a correspondence between the anyon parameter and the exclusion parameter which is different from the case of anyons in a magnetic field, discussed in the talk by Jon Magne Leinaas.
anyon,exclusion,neutrons,quantum
Jan Myrheim
4047
Tue, 11 Oct 2016 00:00:01 +0100

18
geometry
topology
spin
statistics
particle
exchange
quantum
exclusion
In this talk Jon Magne Leinaas from University of Oslo reviews some of the basic ideas and questions related to the exchange symmetry of identical particles. This talks begins with discussing the braid description of particle exchange and some of the interesting question this raises with respect to geometry and topology. A particularly interesting question is whether the geometric understanding of particle exchange means that the spinstatistics theorem can be given a purely geometric formulation. Even if that so far has not been done, the correct relation between spin and statistics seems in some ways natural from the geometric point of view, as he will discuss. In the last part he will focus on the dynamics of systems of anyons in condensed matter systems, where the physical space has the character of a phase space rather than a configuration space. A semiclassical description is discussed, where the anyon parameter is coupled to an exclusion effect, which in the quantum description is known as exclusion statistics.
http://rss.oucs.ox.ac.uk/tag:20190327:164808:000:file:306858:video
http://media.podcasts.ox.ac.uk/physics/fermionic2016/20160420jon_magne_leinaas_tuesday.mp4
In this talk Jon Magne Leinaas from University of Oslo reviews some of the basic ideas and questions related to the exchange symmetry of identical particles.
In this talk Jon Magne Leinaas from University of Oslo reviews some of the basic ideas and questions related to the exchange symmetry of identical particles. This talks begins with discussing the braid description of particle exchange and some of the interesting question this raises with respect to geometry and topology. A particularly interesting question is whether the geometric understanding of particle exchange means that the spinstatistics theorem can be given a purely geometric formulation. Even if that so far has not been done, the correct relation between spin and statistics seems in some ways natural from the geometric point of view, as he will discuss. In the last part he will focus on the dynamics of systems of anyons in condensed matter systems, where the physical space has the character of a phase space rather than a configuration space. A semiclassical description is discussed, where the anyon parameter is coupled to an exclusion effect, which in the quantum description is known as exclusion statistics.
geometry,topology,spin,statistics,particle,exchange,quantum,exclusion,20161011
Jon Magne Leinaas
4706
Tue, 11 Oct 2016 00:00:00 +0100