A quantum Monte-Carlo method for fermions, free of discretization errors

TL;DR

This paper introduces a new quantum Monte-Carlo method for fermions that eliminates discretization errors and is applicable to various interactions at both ground-state and finite temperatures, enhancing computational efficiency.

Contribution

The paper presents an exact, low-rank matrix-based quantum Monte-Carlo approach for fermions that removes discretization errors and broadens applicability to complex interactions.

Findings

Successfully applied to an analytically solvable pairing model

Demonstrated effectiveness on the Hubbard model

Achieved faster calculations due to low-rank decomposition

Abstract

In this work we present a novel quantum Monte-Carlo method for fermions, based on an exact decomposition of the Boltzmann operator $exp(-\beta H)$. It can be seen as a synthesis of several related methods. It has the advantage that it is free of discretization errors, and applicable to general interactions, both for ground-state and finite-temperature calculations. The decomposition is based on low-rank matrices, which allows faster calculations. As an illustration, the method is applied to an analytically solvable model (pairing in a degenerate shell) and to the Hubbard model.