Quantum kinetic Ising models

TL;DR

This paper introduces a quantum generalization of classical kinetic Ising models using quantum many-body master equations, linking their dynamics to Hamiltonian systems with entanglement properties.

Contribution

It presents a novel quantum extension of kinetic Ising models, connecting their dynamics to Hamiltonian systems and analyzing their ground states and entanglement features.

Findings

Ground states are well described by matrix product states.

Critical properties of the Hamiltonians are discussed.

Entanglement properties of low energy states are analyzed.

Abstract

We introduce a quantum generalization of classical kinetic Ising models, described by a certain class of quantum many body master equations. Similarly to kinetic Ising models with detailed balance that are equivalent to certain Hamiltonian systems, our models reduce to a set of Hamiltonian systems determining the dynamics of the elements of the many body density matrix. The ground states of these Hamiltonians are well described by matrix product, or pair entangled projected states. We discuss critical properties of such Hamiltonians, as well as entanglement properties of their low energy states.