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

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.

arXiv comment12 pages, 4 figures, 1 table; final version

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• High-precision numerical solution of the Fermi polaron problem and large-order behavior of its diagrammatic series
• Density waves in strongly correlated quantum chains
• Competing Orders and Unconventional Criticality in the Su-Schrieffer-Heeger Model
• Quantum Monte Carlo simulation of spin-boson models using wormhole updates
• Directed-Loop Quantum Monte Carlo Method for Retarded Interactions
• Valence-Bond Order in a Honeycomb Antiferromagnet Coupled to Quantum Phonons
• Thermal and quantum lattice fluctuations in Peierls chains
• Fidelity susceptibility for Lifshitz geometries via Lifshitz Holography
• Quantum phase diagrams of Dicke-Ising models by a wormhole algorithm
• Metal-insulator transition of spinless fermions coupled to dispersive optical bosons