Entanglement Hamiltonian of Many-body Dynamics in Strongly-correlated Systems

TL;DR

This paper investigates the evolution of entanglement in strongly correlated quantum systems after a quench, revealing how entanglement propagates via particle flow and approaches thermal equilibrium, with insights supported by conformal field theory.

Contribution

It introduces a detailed analysis of the entanglement Hamiltonian during non-equilibrium dynamics, linking entanglement propagation to particle flow and thermalization in many-body systems.

Findings

Entanglement spreading is carried by particle flow, as indicated by a current operator in the entanglement Hamiltonian.

Subsystems reach a steady state with an entanglement Hamiltonian converging to a thermal ensemble.

Entanglement temperature in the steady state is spatially uniform, indicating equilibrium.

Abstract

A powerful perspective in understanding non-equilibrium quantum dynamics is through the time evolution of its entanglement content. Yet apart from a few guiding principles for the entanglement entropy, to date, not much else is known about the refined characters of entanglement propagation. Here, we unveil signatures of the entanglement evolving and information propagation out-of-equilibrium, from the view of entanglement Hamiltonian. As a prototypical example, we study quantum quench dynamics of a one-dimensional Bose-Hubbard model by means of time-dependent density-matrix renormalization group simulation. Before reaching equilibration, it is found that a current operator emerges in entanglement Hamiltonian, implying that entanglement spreading is carried by particle flow. In the long-time limit subsystem enters a steady phase, evidenced by the dynamic convergence of the entanglement Hamiltonian to the expectation of a thermal ensemble. Importantly, entanglement temperature of steady state is spatially independent, which provides an intuitive trait of equilibrium. We demonstrate that these features are consistent with predictions from conformal field theory. These findings not only provide crucial information on how equilibrium statistical mechanics emerges in many-body dynamics, but also add a tool to exploring quantum dynamics from perspective of entanglement Hamiltonian.