Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the functional renormalization group

SciPost Physics, Journal Year: 2025, Volume and Issue: 18(3)

Published: March 4, 2025

We extend the recently introduced single-boson exchange formulation to computation of self-energy from Schwinger–Dyson equation (SDE). In particular, we derive its expression both in diagrammatic and physical channels. The simple form SDE, involving only bosonic propagator fermion-boson vertex, but not rest function, allows for an efficient numerical implementation. furthermore discuss implications a truncated unity solver, where restricted number factors introduces information loss projection momentum dependence that general affects equivalence between different channel representations. application functional renormalization group, find convergence depends on representation SDE. For two-dimensional Hubbard model at weak coupling, pseudogap opening driven by antiferromagnetic fluctuations is captured already single ( s s -wave) factor magnetic representation, differently density superconducting

Language: Английский

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Two-particle calculations with quantics tensor trains: Solving the parquet equations

Physical Review Research, Journal Year: 2025, Volume and Issue: 7(2)

Published: April 24, 2025

We present an application of quantics tensor trains (QTTs) and cross interpolation (TCI) to the solution a full set self-consistent equations for multivariate functions, so-called parquet equations. show that steps needed evaluate (Bethe-Salpeter equations, equation, Schwinger-Dyson equation) can be decomposed into basic operations on QTT-TCI compressed objects. The repeated these does not lead loss accuracy beyond specified tolerance iterative scheme converges even numerically demanding parameters. As examples, we take Hubbard model in atomic limit single impurity Anderson model, where objects two-particle vertices, depend three frequencies, but momenta. results this approach is able overcome major computational bottlenecks standard numerical methods. applied methods allow exponential increase number grid points included calculations, corresponding reduction error, linear cost. Published by American Physical Society 2025

Language: Английский

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Dynamical vertex approximation for many-electron systems with spontaneously broken SU(2) symmetry

Physical review. B./Physical review. B, Journal Year: 2021, Volume and Issue: 104(8)

Published: Aug. 12, 2021

While it is commonly assumed that correlation effects in quantum materials get partly mitigated by the onset of magnetic order, precise role played strong correlations spontaneous symmetry-broken phases remains largely unexplored. Here, authors' generalization one most used diagrammatic extensions dynamical mean-field theory to treat ordered provides a powerful tool unveil spectroscopic signatures electronic strongly correlated magnets, as highlighted preliminary results for testbed cases.

Language: Английский

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The plain and simple parquet approximation: single-and multi-boson exchange in the two-dimensional Hubbard model

The European Physical Journal B, Journal Year: 2022, Volume and Issue: 95(4)

Published: April 1, 2022

Abstract The parquet approach to vertex corrections is unbiased but computationally demanding. Most applications are therefore restricted small cluster sizes or rely on various simplifying approximations. We have recently shown that the bosonization of diagrams provides interpretative and algorithmic advantages over original purely fermionic formulation. Here, we present first results numerical implementation this method by applying it half-filled Hubbard model square lattice at weak coupling. improved performance allows us evaluate approximation for a $$16\times 16$$ 16 × lattice, retaining full momentum frequency structure functions. discuss their symmetries consider parametrizations dependence using truncated-unity approximation. Graphical abstract

Language: Английский

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General Shiba mapping for on-site four-point correlation functions

Physical Review Research, Journal Year: 2024, Volume and Issue: 6(3)

Published: July 15, 2024

By applying the Shiba mapping on two-particle level, we derive relation between local four-point correlation functions of bipartite lattice models with on-site electronic repulsion and those corresponding attractive interaction in most general setting. In particular, extend results [], which were limited to rather specific situation static limit strictly particle-hole symmetric models, (i) by explicitly including magnetic field different values chemical potentials, (ii) considering full dependence generalized susceptibilities transfer (bosonic) Matsubara frequency. The derived formalism is then applied, as a relevant benchmark, Hubbard atom investigating properties divergences its irreducible vertex function potential applied field. resulting phase diagrams provide an insightful compass for future studies breakdown self-consistent perturbation expansion beyond high-symmetric regimes. Published American Physical Society 2024

Language: Английский

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