On quenches to the critical point of the three states Potts model -- Matrix Product State simulations and CFT

TL;DR

This paper investigates the out-of-equilibrium entanglement dynamics of the three-state Potts model after a quantum quench, comparing numerical matrix product state results with conformal field theory predictions, revealing limitations of CFT in describing long-time entanglement.

Contribution

It provides the first numerical comparison of CFT predictions with MPS simulations for the three-state Potts model after a quantum quench, highlighting where CFT fails to describe entanglement at long times.

Findings

CFT does not accurately describe the long-time entanglement spectrum of the Potts model.

Numerical MPS simulations show CFT matches short-time entanglement dynamics.

The study extends understanding of out-of-equilibrium behavior in non-Ising critical models.

Abstract

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 behaviour 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 find that, in this case, the entanglement spectrum is indeed described by the CFT at long times.