Enforcing conservation laws in nonequilibrium cluster perturbation theory

TL;DR

This paper develops a conservation-law respecting extension of nonequilibrium cluster perturbation theory (CPT) that ensures energy, particle number, and spin are conserved during simulations, improving the accuracy of modeling quantum many-body dynamics.

Contribution

The authors introduce a self-consistent, conserving CPT framework that enforces macroscopic conservation laws in nonequilibrium quantum systems, extending the original CPT approach.

Findings

Conservation laws are incorporated as local continuity equations.

The method respects conservation of energy, particle number, and spin.

Enforcing conservation laws significantly alters the dynamics, leading to more realistic relaxation behavior.

Abstract

Using the recently introduced time-local formulation of the nonequilibrium cluster perturbation theory (CPT), we construct a generalization of the approach such that macroscopic conservation laws are respected. This is achieved by exploiting the freedom for the choice of the starting point of the all-order perturbation theory in the inter-cluster hopping. The proposed conserving CPT is a self-consistent propagation scheme which respects the conservation of energy, particle number and spin, which treats short-range correlations exactly up to the linear scale of the cluster, and which represents a mean-field-like approach on length scales beyond the cluster size. Using Green's functions, conservation laws are formulated as local continuity equations for the local spin-dependent particle and the doublon density. We consider them as conditional equations to self-consistently fix the time-dependent intra-cluster one-particle parameters. Thanks to the intrinsic causality of the CPT, this can be set up as a step-by-step time propagation scheme with a computational effort scaling linearly with the maximum propagation time and exponentially in the cluster size. As a proof of concept, we consider the dynamics of the two-dimensional, particle-hole-symmetric Hubbard model following a weak interaction quench by simply employing two-site clusters only. Conservation laws are satisfied by construction. We demonstrate that enforcing them has strong impact on the dynamics. While the doublon density is strongly oscillating within plain CPT, a monotonic relaxation is observed within the conserving CPT.