Algorithmic approach to diagrammatic expansions for real-frequency evaluation of susceptibility functions

Taheridehkordi, Amir; Curnoe, S. H.; LeBlanc, James

doi:10.1103/physrevb.102.045115

Cited by 29 publications

(7 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this work we have presented results for singleparticle quantities from partial diagrammatic expansions of the 2D Hubbard model, for both Matsubara and real frequencies, made possible by recent advancements in symbolic tools. 13,17,41 Thanks to exact results, at extremely high order, 12 we compute and contrast the direct expansion of the Green's function against the use of the Dyson series expansion. We compute the single particle properties of the half-filled model including up to sixth order contributions, a feat that requires the generation and evaluation of ∼ 10 6 analytic expressions.…”

Section: Discussionmentioning

confidence: 99%

Single particle properties of the 2D Hubbard model for real frequencies at weak coupling: Breakdown of the Dyson series for partial self-energy expansions

McNiven,

Andrews,

LeBlanc

2021

Preprint

View full text Add to dashboard Cite

We generate the perturbative expansion of the single-particle Green's function and related selfenergy for a half-filled single-band Hubbard model on a square lattice. We invoke algorithmic Matsubara integration to evaluate single-particle quantities for real and Matsubara frequencies and verify results through comparison to existing data on the Matsubara axis. With low order expansions at weak-coupling we observe a number of outcomes expected at higher orders: the opening of a gap, pseudogap behavior, and Fermi-surface reconstruction. Based on low-order perturbations we consider the phase diagram that arises from truncated expansions of the self-energy and Green's function and their relation via the Dyson equation. From Matsubara axis data we observe insulating behavior in direct expansions of the Green's function, while the same order of truncation of the selfenergy produces metallic behavior. This observation is supported by additional calculations for real frequencies. We attribute this difference to the order in which diagrams are implicitly summed in the Dyson series. Our observations for this particular case lead us to question the general utility of the Dyson equation.

show abstract

Section: Discussionmentioning

confidence: 99%

Single particle properties of the 2D Hubbard model for real frequencies at weak coupling: Breakdown of the Dyson series for partial self-energy expansions

McNiven,

Andrews,

LeBlanc

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Automating the generation of the AMI input starting from operators or from a particular diagrammatic expansion can be accomplished,[14, 15,16] but is not intended to become a part of libami. Instead, the necessary components for full automation will be developed using libami as the backend.…”

Section: Extensionsmentioning

confidence: 99%

LIBAMI: Implementation of Algorithmic Matsubara Integration

Elazab,

McNiven,

LeBlanc

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Thus, while the regime at very high temperature is well understood, there is an intermediate temperature regime where currently no reliable calculations exist. Modern DiagMC methods formulated in real frequency (245) promise a resolution of this problem.…”

Section: Bad Metalmentioning

confidence: 99%

The Hubbard model: A computational perspective

Qin,

Schäfer,

Andergassen

et al. 2021

Preprint

View full text Add to dashboard Cite

The Hubbard model is the simplest model of interacting fermions on a lattice and is of similar importance to correlated electron physics as the Ising model is to statistical mechanics or the fruit fly to biomedical science. Despite its simplicity, the model exhibits an incredible wealth of phases, phase transitions, and exotic correlation phenomena. While analytical methods have provided a qualitative description of the model in certain limits, numerical tools have shown impressive progress in achieving quantitative accurate results over the last years. This article gives an introduction to the model, motivates common questions, and illustrates the progress that has been achieved over the last years in revealing various aspects of the correlation physics of the model.

show abstract

Algorithmic approach to diagrammatic expansions for real-frequency evaluation of susceptibility functions

Cited by 29 publications

References 59 publications

Single particle properties of the 2D Hubbard model for real frequencies at weak coupling: Breakdown of the Dyson series for partial self-energy expansions

Single particle properties of the 2D Hubbard model for real frequencies at weak coupling: Breakdown of the Dyson series for partial self-energy expansions

LIBAMI: Implementation of Algorithmic Matsubara Integration

The Hubbard model: A computational perspective

Contact Info

Product

Resources

About