Boson-Exchange Parquet Solver for dual fermions

Krien, Friedrich; Valli, Angelo; Chalupa, Patrick; Capone, Massimo; Lichtenstein, Alexander I.; Toschi, Alessandro

doi:10.48550/arxiv.2008.04184

Cited by 6 publications

(31 citation statements)

References 103 publications

(227 reference statements)

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“…The present paper is in close conjunction with Ref. [39] where the parquet equations for dual fermions [40] have been reformulated. Instead, here we show how the standard parquet approach [4][5][6][7][8][9][10] can be rewritten and connected with the Hedin equations [41].…”

Section: Introductionmentioning

confidence: 78%

“…( 6) and reexpressing everything in terms of the new variables (Λ Uirr , M, ∆), we obtain, analogous to Ref. [39], the parquet equation formulated in terms of…”

Section: A Unified Approach To Vertex Correctionsmentioning

confidence: 88%

“…( 10) of the Hedin formalism, and formulate a unified theory. To this end, we will pinpoint the difference between Λ Uirr and Λ, which is denoted as [39] multi-boson exchange (MBE) diagrams M α (the SBE diagrams ∆ α are not part of Λ Uirr ; Fig. 3 below clarifies the multi-boson character of M ).…”

Section: A Unified Approach To Vertex Correctionsmentioning

confidence: 99%

“…Now we are in a position to formulate a new efficient calculation scheme, called a Boson Exchange Parquet Solver (BEPS), which was introduced for dual fermions in Ref. [39]. The algorithm is as follows (for clarity, we repeat the most relevant equations):…”

Section: Calculation Schemementioning

confidence: 99%

“…An efficient real fermion parquet solver for a quantum impurity model is presented and made available [42]. Similar as for dual fermions [39], this reformulation leads to a substantially improved feasibility of the parquet solution because it removes simultaneously the high-frequency asymptotics [43] and the long-ranged fluctuations [20] from the parquet equations.…”

Section: Introductionmentioning

confidence: 99%

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Tiling with triangles: parquet and $GWγ$ methods unified

Krien,

Kauch,

Held

2020

Preprint

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The parquet formalism and Hedin's GW γ approach are unified into a single theory of vertex corrections, corresponding to a bosonization of the parquet equations. The method has no drawbacks compared to previous parquet solvers but has the significant advantage that the vertex functions decay quickly with frequencies and with respect to distances in the real space. These properties coincide with the respective separation of the length and energy scales of the two-particle correlations into long/short-ranged and high/low-energetic.

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Section: Introductionmentioning

confidence: 78%

“…( 6) and reexpressing everything in terms of the new variables (Λ Uirr , M, ∆), we obtain, analogous to Ref. [39], the parquet equation formulated in terms of…”

Section: A Unified Approach To Vertex Correctionsmentioning

confidence: 88%

Section: A Unified Approach To Vertex Correctionsmentioning

confidence: 99%

Section: Calculation Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Tiling with triangles: parquet and $GWγ$ methods unified

Krien,

Kauch,

Held

2020

Preprint

Self Cite

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

Krien,

Lichtenstein,

Rohringer

2020

Preprint

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We apply the boson exchange parquet solver for dual fermions to the half-filled Hubbard model on a square lattice at small interaction. Our results establish that in this regime nonlocal vertex corrections play an important role in the formation of the pseudogap. Namely, in comparison to the simpler ladder approximation, these additional vertex corrections included in the parquet equations enhance the coupling of spin fluctuations with the quasiparticles. The pseudogap thus opens already at a higher temperature, in quantitative agreement with the numerically exact diagrammatic Monte Carlo. The representation of the parquet diagrams in terms of boson exchange facilitates large lattice sizes and gives rise to an unbiased fluctuation diagnostic of the self-energy, which does not rely on the Fierz ambiguity. The fluctuation diagnostic implies that nodal and antinodal fermions are affected equally by spin fluctuations with the exact commensurate nesting vector (π, π). However, the antinode couples more efficiently to incommensurate fluctuations than the node, leading to the nodal/antinodal dichotomy. We corroborate this finding in terms of a spin-fermion-like calculation.

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Boson-Exchange Parquet Solver for dual fermions

Cited by 6 publications

References 103 publications

Tiling with triangles: parquet and $GWγ$ methods unified

Tiling with triangles: parquet and $GWγ$ methods unified

Beyond quantum cluster theories: multiscale approaches for strongly correlated systems

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

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