Critical Scaling Behaviors of Entanglement Spectra

TL;DR

This paper studies how entanglement spectra evolve after a quantum quench to criticality, revealing distinct finite-size scaling behaviors and universal structures that emerge dynamically in a 1D Ising chain.

Contribution

It introduces a detailed analysis of the dynamical entanglement spectra scaling behaviors and uncovers universal tower structures related to Ising criticality during quantum quenches.

Findings

Entanglement spectra scale as l^{-1} in dynamical equilibrium, faster than in static cases.

Universal tower structure of Ising criticality emerges at long times.

Operator-state correspondence appears in quantum dynamics.

Abstract

We investigate the evolution of entanglement spectra under a global quantum quench from a short-range correlated state to the quantum critical point. Motivated by the conformal mapping, we find that the dynamical entanglement spectra demonstrate distinct finite-size scaling behaviors from the static case. As a prototypical example, we compute real-time dynamics of the entanglement spectra of a one-dimensional transverse-field Ising chain. Numerical simulation confirms that, the entanglement spectra scale with the subsystem size $l$ as $\sim l^{-1}$ for the dynamical equilibrium state, much faster than $\propto \log^{-1} l$ for the critical ground state. In particular, as a byproduct, the entanglement spectra at the long time limit faithfully gives universal tower structure of underlying Ising criticality, which shows the emergence of operator-state correspondence in the quantum dynamics.