Applications of Cluster Perturbation Theory Using Quantum Monte Carlo Data

TL;DR

This paper explores the use of quantum Monte Carlo data within cluster perturbation theory to calculate spectral functions of the Hubbard model, enabling larger cluster sizes and potentially more accurate physics insights despite stochastic errors.

Contribution

It introduces a methodology combining quantum Monte Carlo with cluster perturbation theory for improved spectral function calculations in the Hubbard model.

Findings

Quantum Monte Carlo enables larger cluster sizes in spectral calculations.

Results show good agreement with exact diagonalization for small clusters.

The approach captures more relevant physics due to increased cluster size.

Abstract

We study cluster perturbation theory [Phys. Rev. Lett. \textbf{84}, 522 (2000)] when auxiliary field quantum Monte Carlo method is used for solving the cluster hamiltonian. As a case study, we calculate the spectral functions of the Hubbard model in one and two dimensions and compare our results for the spectral functions to results obtained using exact diagonalization to solve the cluster hamiltonian. The main advantage of using quantum Monte Carlo results as a starting point is that the initial cluster size can be taken to be considerably larger and hence potentially capture more of the relevant physics. The drawback is that quantum Monte Carlo methods yield results at {\it imaginary} times with stochastic errors.