Entanglement Hamiltonian during a domain wall melting in the free Fermi chain

TL;DR

This paper investigates the evolution of the entanglement Hamiltonian during domain wall melting in a 1D free Fermi chain, combining quantum hydrodynamics and numerical lattice calculations to understand its scaling behavior.

Contribution

It introduces a field theory approach to describe the entanglement Hamiltonian during domain wall melting, validated by high-precision numerical simulations.

Findings

Effective field theory accurately describes the entanglement Hamiltonian in the scaling limit.

Numerical calculations confirm the field theory results when summing over all relevant hoppings.

The approach provides insights into the dynamics of entanglement in free fermion systems.

Abstract

We study the unitary time evolution of the entanglement Hamiltonian of a free Fermi lattice gas in one dimension initially prepared in a domain wall configuration. To this aim, we exploit the recent development of quantum fluctuating hydrodynamics. Our findings for the entanglement Hamiltonian are based on the effective field theory description of the domain wall melting and are expected to exactly describe the Euler scaling limit of the lattice gas. However, such field theoretical results can be recovered from high-precision numerical lattice calculations only when summing appropriately over all the hoppings up to distant sites.