# Quantum kinetic perturbation theory for near-integrable spin chains with weak long-range interactions

## TL;DR

This paper introduces a perturbative quantum kinetic approach to study the relaxation dynamics of weakly long-range interacting spin chains, enabling high-accuracy simulations of spin correlations and thermalization processes.

## Contribution

It develops a novel perturbative scheme based on quantum kinetic equations for near-integrable spin chains with long-range interactions, including multiple truncation levels and benchmarking.

## Key findings

- The method accurately captures prethermalization and thermalization dynamics.
- It allows simulations of systems with around 100 sites for moderate times.
- The approach can be extended to other weakly non-integrable spin models.

## Abstract

For a transverse-field Ising chain with weak long-range interactions we develop a perturbative scheme, based on quantum kinetic equations, around the integrable nearest-neighbour model. We introduce, discuss, and benchmark several truncations of the time evolution equations up to eighth order in the Jordan-Wigner fermionic operators. The resulting set of differential equations can be solved for lattices with $O(10^2)$ sites and facilitates the computation of spin expectation values and correlation functions to high accuracy, at least for moderate timescales. We use this scheme to study the relaxation dynamics of the model, involving prethermalisation and thermalisation. The techniques developed here can be generalised to other spin models with weak integrability-breaking terms.