Local quantum channels giving rise to quasi-local Gibbs states

• URL: http://arxiv.org/abs/2408.08672v1
• Date: Fri, 16 Aug 2024 11:30:29 GMT
• Title: Local quantum channels giving rise to quasi-local Gibbs states
• Authors: Itai Arad, Raz Firanko, Omer Gurevich,
• Abstract summary: We study the steady-state properties of quantum channels with local Kraus operators. A repeated application of these channels can be seen as a simple model for the thermalization process of a many-body system.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the steady-state properties of quantum channels with local Kraus operators. We consider a large family that consists of general ergodic 1-local (non-interacting) terms and general 2-local (interacting) terms. Physically, a repeated application of these channels can be seen as a simple model for the thermalization process of a many-body system. We study its steady state perturbatively by interpolating between the 1-local and 2-local channels with a perturbation parameter $\epsilon$. We prove that under very general conditions, these states are Gibbs states of a quasi-local Hamiltonian. Expanding this Hamiltonian as a series in $\epsilon$, we show that the $k$'th order term corresponds to a $(k+1)$-local interaction term in the Hamiltonian, which follows the same interaction graph as the Kraus channel. We also prove a complementary result suggesting the existence of an interaction strength threshold, under which the total weight of the high-order terms in the Hamiltonian decays exponentially fast. This result also implies a quasi-polynomial classical algorithm for computing the expectation value of local observables in such steady states. Finally, we also present numerical simulations of various channels that support our theoretical claims.

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