Footprints of impurity quantum phase transitions in quantum Monte Carlo statistics

Interacting single-level quantum dots connected to BCS superconducting leads represent 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 (QPT). 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 QPT. 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.

Automated summary

Studying the quantum phase transition in systems with interacting single-level quantum dots connected to BCS superconducting leads, statistical analysis using the continuous-time hybridization expansion quantum Monte Carlo algorithm was conducted to reveal thermodynamic mixing of two phases at low but finite temperatures. The deviation from the ideal Gaussian shape in the expansion order histograms suggests a bimodal nature reflecting the interplay between the correlation effects and electron pairing.