Footprints of impurity quantum phase transitions in quantum Monte Carlo statistics

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.

13 pages, 8 figures

References in corpus (12)

• Continuous-time Monte Carlo methods for quantum impurity models
• The numerical renormalization group method for quantum impurity systems
• Quantum Monte Carlo Impurity Solver for Cluster DMFT and Electronic Structure Calculations in Adjustable Base
• Supercurrent reversal in quantum dots
• Critical Current 0-$\pi$ Transition in Designed Josephson Quantum Dot Junctions
• Fidelity susceptibility made simple: A unified quantum Monte Carlo approach
• $i$QIST: An open source continuous-time quantum Monte Carlo impurity solver toolkit
• Study of 0-$\pi$ phase transition in hybrid superconductor-InSb nanowire quantum dot devices
• $i$QIST v0.7: An open source continuous-time quantum Monte Carlo impurity solver toolkit
• Josephson-phase-controlled interplay between correlation effects and electron pairing in a three-terminal nanostructure
• Detecting phase transitions and crossovers in Hubbard models using the fidelity susceptibility
• Numerical renormalization group calculation of impurity internal energy and specific heat of quantum impurity models

Cited by in corpus (1)

• Evolution of the Andreev bands in the half-filled superconducting periodic Anderson model