Local Operator Entanglement in Spin Chains

Kavli Affiliate: Masahiro Nozaki

| First 5 Authors: Eric Mascot, Masahiro Nozaki, Masaki Tezuka, ,

| Summary:

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.

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