Single- and two-particle finite size effects in interacting lattice systems

TL;DR

This paper compares finite size effect mitigation techniques in quantum simulations, demonstrating that twist-averaging and dynamical cluster approximations converge to the same limit but differ in convergence speed, with embedding theories effectively managing finite size effects.

Contribution

It unifies the understanding of twist-averaging and dynamical cluster methods, showing their equivalence and effectiveness in reducing finite size effects in interacting lattice systems.

Findings

All methods converge to the same thermodynamic limit.

Convergence speed varies among techniques.

Embedding theories effectively manage finite size effects.

Abstract

Simulations of extended quantum systems are typically performed by extrapolating results of a sequence of finite-system-size simulations to the thermodynamic limit. In the quantum Monte Carlo community, twist-averaging was pioneered as an efficient strategy to eliminate one-body finite size effects. In the dynamical mean field community, cluster generalizations of the dynamical mean field theory were formulated to study systems with non-local correlations. In this work, we put the twist-averaging and the dynamical cluster approximation variant of the dynamical mean field theory onto equal footing, discuss commonalities and differences, and compare results from both techniques to the standard periodic boundary technique. At the example of Hubbard-type models with local, short-range and Yukawa-like longer range interactions we show that all methods converge to the same limit, but that the convergence speed differs in practice. We show that embedding theories are an effective tool for managing both one-body and two-body finite size effects, in particular if interactions are averaged over twist angles.