Local Operator Entanglement in Spin Chains

TL;DR

This paper studies how local perturbations spread in quantum spin chains, revealing light cone dynamics in clean systems and localization effects in disordered systems, with implications for quantum thermalization and computation.

Contribution

It provides a detailed analysis of operator mutual information dynamics in spin chains, including the effects of disorder and localization, and introduces an effective Hamiltonian description for disordered regimes.

Findings

Early-time evolution follows light cone behavior in the Ising model.

Late-time mutual information approaches Page's value for random states.

Strong disorder induces many-body localization, preventing information spread.

Abstract

Understanding how and whether local perturbations can affect the entire quantum system is a fundamental step in understanding non-equilibrium phenomena such as thermalization. This knowledge of non-equilibrium phenomena is applicable for quantum computation, as many quantum computers employ non-equilibrium processes for computations. In this paper, we investigate the evolution of bi- and tripartite operator mutual information of the time-evolution operator and the Pauli spin operators in the one-dimensional Ising model with magnetic field and the disordered Heisenberg model to study the properties of quantum circuits. In the Ising model, the early-time evolution qualitatively follows an effective light cone picture, and the late-time value is well described by Page's value for a random pure state. In the Heisenberg model with strong disorder, we find that many-body localization prevents the information from propagating and being delocalized. We also find an effective Ising Hamiltonian that describes the time evolution of bi- and tripartite operator mutual information for the Heisenberg model in the large disorder regime.