Efficient continuous-time quantum Monte Carlo algorithm for fermionic lattice models

TL;DR

This paper introduces an efficient continuous-time quantum Monte Carlo algorithm for fermionic lattice models that matches the scaling of discrete-time methods but avoids discretization errors, enabling more precise low-temperature simulations.

Contribution

The authors develop a CT-QMC algorithm for fermionic lattice models with linear scaling, improving efficiency and accuracy over existing methods.

Findings

Achieves linear scaling with inverse temperature β.

Eliminates systematic errors from time discretization.

Enables more precise simulations of large systems at low temperatures.

Abstract

Efficient continuous time quantum Monte Carlo (CT-QMC) algorithms that do not suffer from time discretization errors have become the state-of-the-art for most discrete quantum models. They have not been widely used yet for fermionic quantum lattice models, such as the Hubbard model, due to a suboptimal scaling of $O(\beta^3)$ with inverse temperature $\beta$, compared to the linear scaling of discrete time algorithms. Here we present a CT-QMC algorithms for fermionic lattice models that matches the scaling of discrete-time methods but is more efficient and free of time discretization errors. This provides an efficient simulation scheme that is free from the systematic errors opening an avenue to more precise studies of large systems at low temperatures.