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.

arXiv comment13 pages, 8 figures

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• Effective low-energy models for superconducting impurity systems
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains
• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots
• Evolution of the Andreev bands in the half-filled superconducting periodic Anderson model