Determinantal Quantum Monte Carlo solver for Cluster Perturbation Theory

TL;DR

This paper introduces a Determinantal Quantum Monte Carlo solver for Cluster Perturbation Theory, enabling larger cluster sizes, temperature dependence studies, and more extensive simulations of fermionic models with local interactions.

Contribution

The paper presents a novel DQMC solver for CPT that improves upon existing methods by reducing finite size effects and allowing larger, temperature-dependent simulations.

Findings

DQMC reduces finite size effects compared to ED.

CPT+DQMC enables larger cluster simulations.

Method outperforms standard DQMC and CPT+ED in benchmarks.

Abstract

Cluster Perturbation Theory (CPT) is a technique for computing the spectral function of fermionic models with local interactions. By combining the solution of the model on a finite cluster with perturbation theory on intra-cluster hoppings, CPT provides access to single-particle properties with arbitrary momentum resolution while incurring low computational cost. Here, we introduce Determinantal Quantum Monte Carlo (DQMC) as a solver for CPT. Compared to the standard solver, exact diagonalization (ED), the DQMC solver reduces finite size effects through utilizing larger clusters, allows study of temperature dependence, and enables large-scale simulations of a greater set of models. We discuss the implementation of the DQMC solver for CPT and benchmark the CPT+DQMC method for the attractive and repulsive Hubbard models, showcasing its advantages over standard DQMC and CPT+ED simulations.