Local quantum channels giving rise to quasi-local Gibbs states
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908306353684480 |
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| author | Arad, Itai Firanko, Raz Gurevich, Omer |
| author_facet | Arad, Itai Firanko, Raz Gurevich, Omer |
| contents | 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 $ε$. We prove that under very general conditions, these states are Gibbs states of a quasi-local Hamiltonian. Expanding this Hamiltonian as a series in $ε$, 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. For sufficiently small $ε$, this implies both exponential decay of local correlation functions and a classical algorithm for computing expectation value of local observables in such steady states. Finally, we present numerical simulations of various channels that support our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08672 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local quantum channels giving rise to quasi-local Gibbs states Arad, Itai Firanko, Raz Gurevich, Omer Quantum Physics Statistical Mechanics Mathematical Physics 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 $ε$. We prove that under very general conditions, these states are Gibbs states of a quasi-local Hamiltonian. Expanding this Hamiltonian as a series in $ε$, 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. For sufficiently small $ε$, this implies both exponential decay of local correlation functions and a classical algorithm for computing expectation value of local observables in such steady states. Finally, we present numerical simulations of various channels that support our theoretical results. |
| title | Local quantum channels giving rise to quasi-local Gibbs states |
| topic | Quantum Physics Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2408.08672 |