Quantum kinetic Ising models

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.

20 pages, 4 figures, minor improvements, accepted in New Journal of Physics

References in corpus (10)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• A Rydberg Quantum Simulator
• Matrix product states represent ground states faithfully
• Area laws in quantum systems: mutual information and correlations
• Criticality, the area law, and the computational power of PEPS
• Strong dissipation inhibits losses and induces correlations in cold molecular gases
• Entropy scaling and simulability by Matrix Product States
• An area law for the entropy of low-energy states
• Stochastic exclusion processes versus coherent transport

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• Many body physics from a quantum information perspective
• Unifying Collisional Models and the Monte Carlo Metropolis Method: Algorithms for Dynamics of Open Quantum Systems
• Random Transverse Field Effects on Magnetic Noise in Spin Systems
• A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems