Footprints of impurity quantum phase transitions in quantum Monte Carlo statistics

TL;DR

This paper investigates how impurity quantum phase transitions influence the statistics of quantum Monte Carlo perturbation expansions in a quantum dot system, revealing phase mixing effects at finite temperatures.

Contribution

It introduces an analysis of perturbation order statistics in quantum Monte Carlo simulations near impurity quantum phase transitions, highlighting bimodal histogram features.

Findings

Histograms of expansion order become bimodal near phase transition.

Moments of the histogram deviate from Gaussian, indicating phase mixing.

Insights into thermodynamic phase coexistence at finite temperatures.

Abstract

Interacting single-level quantum dot connected to BCS superconducting leads represents a well-controllable system to study the interplay between the correlation effects and the electron pairing that can result in a $0-\pi$ (singlet-doublet) quantum phase transition. The physics of this system can be well described by the impurity Anderson model. We present an analysis of the statistics of the perturbation expansion order of the continuous-time hybridization expansion quantum Monte Carlo algorithm in the vicinity of such a first-order impurity quantum phase transition. By calculating the moments of the histograms of the expansion order which deviate from the ideal Gaussian shape, we provide an insight into the thermodynamic mixing of the two phases at low but finite temperatures which is reflected in the bimodal nature of the histograms.