Ground-state dispersion and density of states from path-integral Monte Carlo. Application to the lattice polaron

TL;DR

This paper introduces a new formula linking ground-state dispersion to path distributions in quantum Monte Carlo, enabling direct measurement of spectra without complex analysis, demonstrated on lattice polarons across multiple dimensions.

Contribution

A novel formula that relates ground-state dispersion to path distributions, allowing direct Monte Carlo measurement without analytical continuation.

Findings

Exact polaron spectra computed in 1D, 2D, and 3D.

Polaron density of states significantly deviates from free-particle shape in the adiabatic regime.

Method simplifies spectral calculations in many-body quantum systems.

Abstract

A formula is derived that relates the ground-state dispersion of a many-body system with the end-to-end distribution of paths with open boundary conditions in imaginary time. The formula does not involve the energy estimator. It allows direct measurement of the ground-state dispersion by quantum Monte Carlo methods without analytical continuation or auxiliary fitting. The formula is applied to the lattice polaron problem. The exact polaron spectrum and density of states are calculated for several models in one, two, and three dimensions. In the adiabatic regime of the Holstein model, the polaron density of states deviates spectacularly from the free-particle shape.