Constrained sampling method for analytic continuation

TL;DR

This paper introduces a novel constrained sampling method for analytic continuation of quantum Monte Carlo data, effectively reducing entropy-related distortions and accurately reconstructing spectral functions with identifiable peaks.

Contribution

It presents a new constrained sampling approach that improves spectral function reconstruction by suppressing entropy and enforcing peak constraints, outperforming previous methods.

Findings

Accurately reproduces the dynamic structure factor of the Heisenberg chain.

Achieves good agreement with Bethe Ansatz and exact diagonalization results.

Effectively suppresses distortions caused by configurational entropy.

Abstract

A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large number of delta-functions, treated as a statistical-mechanics problem, it avoids distortions caused by (as demonstrated here) configurational entropy in previous sampling methods. The key development is the suppression of entropy by constraining the spectral weight to within identifiable optimal bounds and imposing a set number of peaks. As a test case, the dynamic structure factor of the S=1/2 Heisenberg chain is computed. Very good agreement is found with Bethe Ansatz results in the ground state (including a sharp edge) and with exact diagonalization of small systems at elevated temperatures.