Entanglement dynamics of thermofield double states in integrable models

TL;DR

This paper investigates the entanglement evolution of thermofield double states in integrable models, proposing a semiclassical formula validated through numerical tests on spin chains, revealing insights into quantum quench dynamics.

Contribution

It introduces a conjectured semiclassical formula for entanglement dynamics in integrable models, applicable to both discrete and continuous theories, and validates it with numerical simulations.

Findings

Excellent agreement with free fermion results in XY-model

Good agreement with iTEBD in XXZ model

Finite-time effects cause small discrepancies in some parameter regimes

Abstract

We study the entanglement dynamics of thermofield double (TFD) states in integrable spin chains and quantum field theories. We show that, for a natural choice of the Hamiltonian eigenbasis, the TFD evolution may be interpreted as a quantum quench from an initial state which is low-entangled in the real-space representation and displays a simple quasiparticle structure. Based on a semiclassical picture analogous to the one developed for standard quantum quenches, we conjecture a formula for the entanglement dynamics, which is valid for both discrete and continuous integrable field theories, and expected to be exact in the scaling limit of large space and time scales. We test our conjecture in two prototypical examples of integrable spin chains, where numerical tests are possible. First, in the XY-model, we compare our predictions with exact results obtained by mapping the system to free fermions, finding excellent agreement. Second, we test our conjecture in the interacting XXZ Heisenberg model, against numerical iTEBD calculations. For the latter, we generally find good agreement, although, for some range of the system parameters and within the accessible simulation times, some small discrepancies are visible, which we attribute to finite-time effects.