Entanglement renormalization of thermofield double states

• URL: http://arxiv.org/abs/2104.00693v1
• Date: Thu, 1 Apr 2021 18:00:01 GMT
• Title: Entanglement renormalization of thermofield double states
• Authors: Cheng-Ju Lin, Zhi Li, Timothy H. Hsieh
• Abstract summary: Entanglement renormalization is a method for coarse-graining a quantum state in real space. We find an analytically exact renormalization circuit for finite temperature two-dimensional toric code which maps it to a coarse-grained system with a renormalized higher temperature. We apply this scheme to one-dimensional free boson models at a finite temperature and find that the thermofield double corresponding to the critical thermal state is described by a numerically Lifshitz theory.
• Score: 3.245401968358883
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Entanglement renormalization is a method for coarse-graining a quantum state in real space, with the multi-scale entanglement renormalization ansatz (MERA) as a notable example. We obtain an entanglement renormalization scheme for finite-temperature (Gibbs) states by applying MERA to their canonical purification, the thermofield double state. As an example, we find an analytically exact renormalization circuit for finite temperature two-dimensional toric code which maps it to a coarse-grained system with a renormalized higher temperature, thus explicitly demonstrating its lack of topological order. Furthermore, we apply this scheme to one-dimensional free boson models at a finite temperature and find that the thermofield double corresponding to the critical thermal state is described by a Lifshitz theory. We numerically demonstrate the relevance and irrelevance of various perturbations under real space renormalization.

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