Continuous-time Quantum Monte Carlo Approach for Impurity Anderson Models with Phonon-assisted Hybridizations

TL;DR

This paper introduces a continuous-time quantum Monte Carlo method for impurity Anderson models with phonon-assisted hybridizations, enabling analysis of complex electron-phonon interactions and verifying non-Fermi liquid critical behavior.

Contribution

The authors develop a novel Monte Carlo approach for Anderson impurity models with phonons, applicable to multiple phonon modes, and validate it through a benchmark study of the two-channel model.

Findings

Logarithmic divergence of SO(5) susceptibility at critical point

Verification of boundary conformal field theory predictions

Demonstration of method's effectiveness for complex models

Abstract

We develop a continuous-time quantum Monte Carlo method based on a strong-coupling expansion for Anderson impurity models with phonon-assisted hybridizations for arbitrary number of phonon modes. As a benchmark, we investigate the two-channel Anderson model with a single phonon, and numerically demonstrate that an SO(5) susceptibility composed of localized-electron charge and phonon-parity operators diverges logarithmically at the non-Fermi liquid critical point in the model, which verifies the predictions by the boundary conformal field theory[K. Hattori: Phys. Rev. B {\bf 85} (2012) 214411].