Entanglement Renormalization of Thermofield Double States
Abstract
Entanglement renormalization is a method for "coarse graining" a quantum state in real space, with the multiscale entanglement renormalization ansatz as a notable example. We obtain an entanglement renormalization scheme for finitetemperature (Gibbs) states by applying the multiscale entanglement renormalization ansatz to their canonical purification, the thermofield double state. As an example, we find an analytically exact renormalization circuit for a finitetemperature twodimensional toric code that maps it to a coarsegrained system with a renormalized higher temperature, thus explicitly demonstrating its lack of topological order. Furthermore, we apply this scheme to onedimensional 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.
 Publication:

Physical Review Letters
 Pub Date:
 August 2021
 DOI:
 10.1103/PhysRevLett.127.080602
 arXiv:
 arXiv:2104.00693
 Bibcode:
 2021PhRvL.127h0602L
 Keywords:

 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 6 pages of main text + 10 pages of appendices