# Numerical linked cluster expansions for quantum quenches in one dimensional lattices

## TL;DR

This paper applies numerical linked cluster expansions (NLCEs) to analyze one-dimensional lattice systems in thermal equilibrium and after quantum quenches, demonstrating NLCEs' effectiveness in the thermodynamic limit and comparing different expansion methods.

## Contribution

It introduces and compares two NLCE methods for quantum lattice systems, highlighting the site-based NLCE's advantages and divergence issues, and demonstrates NLCEs' superiority over exact diagonalization.

## Key findings

- NLCEs provide accurate thermodynamic limit results.
- Site-based NLCE works best in thermal equilibrium.
- NLCEs outperform exact diagonalization in periodic systems.

## Abstract

We discuss the application of numerical linked cluster expansions (NLCEs) to study one dimensional lattice systems in thermal equilibrium and after quantum quenches from thermal equilibrium states. For the former, we calculate observables in the grand canonical ensemble, and for the latter we calculate observables in the diagonal ensemble. When converged, NLCEs provide results in the thermodynamic limit. We use two different NLCEs - a maximally connected expansion introduced in previous works and a site-based expansion. We compare the effectiveness of both NLCEs. The site-based NLCE is found to work best for systems in thermal equilibrium. However, in thermal equilibrium and after quantum quenches, the site-based NLCE can diverge when the maximally connected one converges. We relate this divergence to the exponentially large number of clusters in the site-based NLCE and the behavior of the weights of observables in those clusters. We discuss the effectiveness of resummations to cure the divergence. Our NLCE calculations are compared to exact diagonalization ones in lattices with periodic boundary conditions. NLCEs are found to outperform exact diagonalization in periodic systems for all quantities studied.