تقرير
Local quantum channels giving rise to quasi-local Gibbs states
| العنوان: | Local quantum channels giving rise to quasi-local Gibbs states |
|---|---|
| المؤلفون: | Arad, Itai, Firanko, Raz, Gurevich, Omer |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Condensed Matter Mathematical Physics Quantum Physics |
| مصطلحات موضوعية: | Quantum Physics, Condensed Matter - Statistical Mechanics, Mathematical Physics |
| الوصف: | 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. Comment: 26 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2408.08672 |
| رقم الأكسشن: | edsarx.2408.08672 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |