Continuous-time quantum Monte Carlo for fermion-boson lattice models: Improved bosonic estimators and application to the Holstein model

TL;DR

This paper advances continuous-time quantum Monte Carlo techniques for fermion-boson lattice models, introducing improved estimators for bosonic observables and applying them to the Holstein model to study phase transitions.

Contribution

It develops new estimators for bosonic observables within the continuous-time Monte Carlo framework and applies these to analyze the Holstein model's phase transition behavior.

Findings

Renormalization of phonon modes across the Peierls transition

Identification of a soft-mode transition in the adiabatic regime

Critical point characterized by minimum phonon kinetic energy and maximum fidelity susceptibility

Abstract

We extend the continuous-time interaction-expansion quantum Monte Carlo method with respect to measuring observables for fermion-boson lattice models. Using generating functionals, we express expectation values involving boson operators, which are not directly accessible because simulations are done in terms of a purely fermionic action, as integrals over fermionic correlation functions. We also demonstrate that certain observables can be inferred directly from the vertex distribution, and present efficient estimators for the total energy and the phonon propagator of the Holstein model. Furthermore, we generalize the covariance estimator of the fidelity susceptibility, an unbiased diagnostic for phase transitions, to the case of retarded interactions. The new estimators are applied to half-filled spinless and spinful Holstein models in one dimension. The observed renormalization of the phonon mode across the Peierls transition in the spinless model suggests a soft-mode transition in the adiabatic regime. The critical point is associated with a minimum in the phonon kinetic energy and a maximum in the fidelity susceptibility.