Real-frequency response functions at finite temperature

TL;DR

This paper introduces a Diagrammatic Monte Carlo method for directly computing finite-temperature response functions on the real-frequency axis, avoiding analytic continuation and applicable to complex, frequency-dependent interacting fermion systems.

Contribution

The authors develop a versatile Monte Carlo approach that computes real-frequency response functions at finite temperature without limitations on system type or diagram summation methods.

Findings

Successfully applied to plasmon linewidth in electron gas

Eliminates need for analytic continuation from Matsubara data

Allows study of spectral densities with controlled accuracy

Abstract

Building on previous developments, we show that the Diagrammatic Monte Carlo technique allows to compute finite temperature response functions directly on the real-frequency axis within any field-theoretical formulation of the interacting fermion problem. There are no limitations on the type and nature of the system's action or whether partial summation and self-consistent treatment of certain diagram classes are used. In particular, by eliminating the need for numerical analytic continuation from a Matsubara representation, our scheme allows to study spectral densities of arbitrary complexity with controlled accuracy in models with frequency-dependent effective interactions. For illustrative purposes we consider the problem of the plasmon line-width in a homogeneous electron gas (jellium).