Spatially Structured Entanglement from Nonequilibrium Thermal Pure States

TL;DR

This paper investigates how spatially inhomogeneous Hamiltonian deformations affect entanglement dynamics in critical quantum systems, revealing universal late-time entanglement patterns and contrasting thermalization behaviors in integrable and non-integrable cases.

Contribution

It introduces a framework for analyzing quantum quench dynamics with inhomogeneous Hamiltonians, demonstrating universal entanglement patterns and connecting field theory results with holographic gravity calculations.

Findings

M"obius deformations lead to thermalization or revivals depending on integrability.

Sine-square and displacement deformations produce late-time graph-like entanglement patterns.

Holographic calculations replicate key features of the quantum dynamics studied.

Abstract

We study quantum quench dynamics in (1+1)-dimensional critical systems, starting from thermal pure states called crosscap states, and evolving them under spatially inhomogeneous Hamiltonians. The spatial inhomogeneity is introduced through a deformation of the Hamiltonian, expressed as linear combinations of the generators of the $SL^{(q)}(2,\mathbb{R})$ subalgebra of the Virasoro algebra. We analyze the free massless Dirac fermion theory and holographic conformal field theory as prototypical examples of integrable and non-integrable dynamics. Consistent with general expectations, "M\"obius-type" deformations lead to thermalization in the non-integrable case, and to periodic revivals in the integrable one. In contrast, "sine-square-type" and "displacement-type" deformations prevent both thermalization and scrambling, instead producing late-time, graph-like entanglement patterns. These patterns emerge from the interplay between the deformed Hamiltonian and the crosscap initial state and appear to be universal: they are determined solely by the deformation profile while remaining largely insensitive to microscopic details. Finally, we perform a holographic calculation in three-dimensional gravity using AdS$_3$/CFT$_2$, which reproduces the main features of our (1+1)-dimensional study.