Diagrammatic Monte Carlo method for many-polaron problems

TL;DR

This paper presents a novel diagrammatic Monte Carlo method for accurately studying many-polaron problems at finite density, including vertex corrections, and demonstrates its effectiveness across various regimes on a square lattice.

Contribution

Introduces the first bold diagrammatic Monte Carlo approach for non-perturbative many-polaron problems at finite density, including high-order vertex corrections.

Findings

Method provides accurate results in the thermodynamic limit across regimes.

Vertex corrections significantly improve theoretical accuracy.

Quasiparticle effective mass increases with density, residue decreases.

Abstract

We introduce the first bold diagrammatic Monte Carlo approach to deal with polaron problems at finite density non-perturbatively, i.e., by including vertex corrections to high orders. Using Holstein model on a square lattice as a prototypical example, we demonstrate that our method is capable of providing accurate results in the thermodynamic limit in all regimes from renormalized Fermi-liquid to single polarons, across the non-adiabatic region where Fermi and Debye energies are of the same order of magnitude. By accounting for vertex corrections the accuracy of theoretical description is increased by orders of magnitude relative to the lowest-order self-consistent Born approximation employed in most studies. We also find that for electron-phonon coupling typical for real materials, the quasiparticle effective mass increases and the quasiparticle residue decreases with increasing the system density.