Quenches to the critical point of the three-state Potts model: Matrix product state simulations and conformal field theory

10 pags., 19 figs.Conformal field theories (CFTs) have been used extensively to understand the physics of critical lattice models at equilibrium. However, the applicability of CFT calculations to the behavior of the lattice systems in the out-of-equilibrium setting is not entirely understood. In this work, we compare the CFT results of the evolution of the entanglement spectrum after a quantum quench with numerical calculations of the entanglement spectrum of the three-state Potts model using matrix product state simulations. Our results lead us to conjecture that CFT does not describe the entanglement spectrum of the three-state Potts model at long times, contrary to what happens in the Ising model. We thus numerically simulate the out-of-equilibrium behavior of the Potts model according to the CFT protocol, i.e., by taking a particular product state and "cooling"it, then quenching to the critical point and finding that, in this case, the entanglement spectrum is indeed described by the CFT at long times.L.T. acknowledges support from the Ramón y Cajal program RYC-2016- 20594, the “Plan Nacional Generación de Conocimiento” PGC2018-095862-B-C22 and and Grant CEX2019-000918- M funded by MCIN/AEI/10.13039/501100011033. This project was supported by the European Union Regional Development Fund within the ERDF Operational Program of Catalunya, Spain (project QUASICAT/QuantumCat, ref. 001- P-001644). J.S acknowledges the Government of Spain (FIS2020-TRANQI and Severo Ochoa CEX2019-000910- S), Fundació Cellex, Fundació Mir-Puig, Generalitat de Catalunya (CERCA, AGAUR SGR 1381)