Scrambling and Recovery of Quantum Information in Inhomogeneous Quenches in Two-dimensional Conformal Field Theories

TL;DR

This paper investigates how quantum information scrambles and can be recovered in two-dimensional conformal field theories under inhomogeneous quenches, revealing robustness of certain correlations and holographic dual descriptions.

Contribution

It introduces a study of quantum quenches via M"obius/sine-square deformation, showing revival of Bell pairs and non-local correlations despite strong scrambling effects.

Findings

Mutual information can revive after initial destruction during quenches.

Steady states exhibit non-local three-party correlations.

Holographic duals involve wormhole growth during dynamics.

Abstract

We study various quantum quench processes induced by the M\"obius/sine-square deformation of the Hamiltonian in two-dimensional conformal field theories starting from the thermofield double state in the two copies of the Hilbert space. These quantum quenches, some of which are directly related to the operator entanglement of the time-evolution operators, allow us to study scrambling and recovery of quantum information. In particular, under the SSD time-evolution, we show from the time-dependence of mutual information that the Bell pairs, initially shared by the subsystems of the two Hilbert spaces, may revive even after the mutual information for small subsystems is completely destroyed by quantum information scrambling dynamics. This mutual information is robust against the strong scrambling dynamics. As a consequence, the steady state has a non-local correlation shared not by any of two parties but by three parties. In the holographic dual description, a wormhole connecting the two Hilbert spaces may non-linearly grow with time during the quantum quenches. We also propose effective pictures that describe the dynamics of mutual information during the time-evolution by inhomogeneous Hamiltonians.