Fluctuation diagnostic of the nodal/antinodal dichotomy in the Hubbard model at weak coupling: a parquet dual fermion approach

Krien, Friedrich; Lichtenstein, Alexander I.; Rohringer, Georg

doi:10.48550/arxiv.2010.05935

“…Some of the latest ideas have not been discussed in the present review. These include but are not limited to the parquet method for the vertex in the boson-fermion representation [309][310][311][312], the atomic approximation of the four-particle irreducible functional method [313], one-particle irreducible functional method [314], nonlocal expansion method [315], and FLEX + DMFT approach [316,317].…”

Section: Discussionmentioning

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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“…Some of the latest ideas have not been discussed in the present review. These include but are not limited to the parquet method for the vertex in the boson-fermion representation, [302][303][304][305] , the atomic approximation of the four-particle irreducible functional method, 306 , one-particle irreducible functional method, 307 nonlocal expansion method. 308 , and FLEX+DMFT approach.…”

Section: Discussionmentioning

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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“…A first pioneering application of the SBE-decomposition used as post-processing tool has been recently presented in Ref. [60], see Fig. 10.…”

Section: The Challenge Of the Non-perturbative Regimementioning

confidence: 99%

How to read between the lines of electronic spectra: the diagnostics of fluctuations in strongly correlated electron systems

Schäfer,

Toschi

2020

Preprint

0

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While calculations and measurements of single-particle spectral properties often offer the most direct route to study correlated electron systems, the underlying physics may remain quite elusive, if information at higher particle levels is not explicitly included. Here, we present a comprehensive overview of the different approaches which have been recently developed and applied to identify the dominant two-particle scattering processes controlling the shape of the oneparticle spectral functions and, in some cases, of the physical response of the system. In particular, we will discuss the underlying general idea, the common threads and the specific peculiarities of all the proposed approaches. While all of them rely on a selective analysis of the Schwinger-Dyson (or the Bethe-Salpeter) equation, the methodological differences originate from the specific two-particle vertex functions to be computed and decomposed. Finally, we illustrate the potential strength of these methodologies by means of their applications the two-dimensional Hubbard model, and we provide an outlook over the future perspective and developments of this route for understanding the physics of correlated electrons.

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Fluctuation diagnostic of the nodal/antinodal dichotomy in the Hubbard model at weak coupling: a parquet dual fermion approach

Cited by 3 publications

References 45 publications

Beyond quantum cluster theories: multiscale approaches for strongly correlated systems

Beyond quantum cluster theories: multiscale approaches for strongly correlated systems

Beyond Quantum Cluster Theories: Multiscale Approaches for Strongly Correlated Systems

How to read between the lines of electronic spectra: the diagnostics of fluctuations in strongly correlated electron systems

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