Many Body Perturbation Theory, Dynamical Mean Field Theory and All That

Biermann, Silke; Lichtenstein, A. I.

doi:10.1002/9783527691036.hsscvol5008

“…A second relevant test problem is the Anderson impurity model [72,73], which is an electronic hopping model hybridised with an impurity site at which there is an energy cost for double occupation. While historically the model has played an important role in our understanding of magnetic impurities and Kondo resonance, it has found a renewed significance within the context of dynamical mean-field theory [74], which underlies modern first principles approaches to strongly correlated materials [75,76]. At its simplest level, dynamical mean-field theory is a framework which allows for an efficient computation of the electronic Green's function of the Hubbard model in the limit of infinite dimensions.…”

Section: Discussionmentioning

confidence: 99%

Capturing strong correlations in spin, electron and local moment systems

Quinn

2019

Preprint

0

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We address the question of identifying degrees of freedom for quantum systems. Typically, quasi-particle descriptions of correlated matter are based upon the canonical algebras of bosons or fermions. Here we highlight that a special class of non-canonical algebras also offer useful quantum degrees of freedom, allowing for the development of quasi-particle descriptions which go beyond the weakly correlated paradigm. We give a broad overview of such algebras for spin, electron and local moment systems, and outline important test problems upon which to develop the framework.

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“…Efforts to combine density functional theory with these post-DMFT/DCA methods are the subject of current active research. Readers interested in these efforts will find useful discussions in references [161,[263][264][265][266][267][268][269][270][271][272].…”

Section: Applicationsmentioning

confidence: 99%

Beyond quantum cluster theories: multiscale approaches for strongly correlated systems

Fotso¹,

Tam²,

Moreno³

2022

Quantum Sci. Technol.

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The degrees of freedom that confer to strongly correlated systems their many intriguing properties also render them fairly intractable through typical perturbative treatments. For this reason, the mechanisms responsible for these technologically promising properties remain mostly elusive. Computational approaches have played a major role in efforts to fill this void. In particular, dynamical mean field theory (DMFT) and its cluster extension, the dynamical cluster approximation (DCA) have allowed significant progress. However, despite all the insightful results of these embedding schemes, computational constraints, such as the minus sign problem in Quantum Monte Carlo (QMC), and the exponential growth of the Hilbert space in exact diagonalization (ED) methods, still limit the length scale within which correlations can be treated exactly in the formalism. A recent advance to overcome these difficulties is the development of multiscale many body approaches whereby this challenge is addressed by introducing an intermediate length scale between the short length scale where correlations are treated exactly using a cluster solver such QMC or ED, and the long length scale where correlations are treated in a mean field manner. At this intermediate length scale correlations can be treated perturbatively. This is the essence of multiscale many-body methods. We will review various implementations of these multiscale many-body approaches, the results they have produced, and the outstanding challenges that should be addressed for further advances.

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“…Efforts to combine density functional theory with these post-DMFT methods are the subject of current active research. Readers interested in these efforts will find them discussed in references [159,[259][260][261][262][263][264][265][266][267][268].…”

Section: Applicationsmentioning

confidence: 99%

Beyond Quantum Cluster Theories: Multiscale Approaches for Strongly Correlated Systems

Fotso¹,

Tam²,

Moreno³

2020

Preprint

0

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The degrees of freedom that confer to strongly correlated systems their many intriguing properties also render them fairly intractable through typical perturbative treatments. For this reason, the mechanisms responsible for these technologically promising properties remain mostly elusive. Computational approaches have played a major role in efforts to fill this void. In particular, dynamical mean field theory (DMFT) and its cluster extension, the dynamical cluster approximation (DCA) have allowed significant progress. However, despite all the insightful results of these embedding schemes, computational constraints, such as the minus sign problem in Quantum Monte Carlo (QMC), and the exponential growth of the Hilbert space in exact diagonalization (ED) methods, still limit the length scale within which correlations can be treated exactly in the formalism. A recent advance to overcome these difficulties is the development of multiscale many body approaches whereby this challenge is addressed by introducing an intermediate length scale between the short length scale where correlations are treated exactly using a cluster solver such QMC or ED, and the long length scale where correlations are treated in a mean field manner. At this intermediate length scale correlations can be treated perturbatively. This is the essence of multiscale many-body methods. We will review various implementations of these multiscale many-body approaches, the results they have produced, and the outstanding challenges that should be addressed for further advances.

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Many Body Perturbation Theory, Dynamical Mean Field Theory and All That

Cited by 3 publications

References 94 publications

Capturing strong correlations in spin, electron and local moment systems

Capturing strong correlations in spin, electron and local moment systems

Beyond quantum cluster theories: multiscale approaches for strongly correlated systems

Beyond Quantum Cluster Theories: Multiscale Approaches for Strongly Correlated Systems

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