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Quantum Physics
Title: Rényi free energy and variational approximations to thermal states
(Submitted on 23 Dec 2020 (v1), last revised 7 Jun 2021 (this version, v2))
Abstract: We propose the construction of thermodynamic ensembles that minimize the R\'enyi free energy, as an alternative to Gibbs states. For large systems, the local properties of these R\'enyi ensembles coincide with those of thermal equilibrium, and they can be used as approximations to thermal states. We provide algorithms to find tensor network approximations to the 2-R\'enyi ensemble. In particular, a matrix-product-state representation can be found by using gradient-based optimization on Riemannian manifolds, or via a non-linear evolution which yields the desired state as a fixed point. We analyze the performance of the algorithms and the properties of the ensembles on one-dimensional spin chains.
Submission history
From: Giacomo Giudice [view email][v1] Wed, 23 Dec 2020 18:16:06 GMT (278kb,D)
[v2] Mon, 7 Jun 2021 13:44:06 GMT (557kb,D)
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