Entanglement Hamiltonian after a local quench

TL;DR

This paper studies how the entanglement Hamiltonian evolves after a local quench in a 1D free fermion system, combining conformal field theory and numerical methods to understand its dynamics.

Contribution

It provides a novel analytical expression for the entanglement Hamiltonian after a local quench and validates it with numerical simulations.

Findings

Analytical expression for entanglement Hamiltonian post-quench

Good agreement between conformal field theory and lattice simulations

Distinct weight functions for left- and right-moving energy components

Abstract

We investigate the dynamics of the entanglement Hamiltonian in a system of one-dimensional free fermions, following a local joining quench of two initially disconnected half-chains in their ground states. Applying techniques of conformal field theory, we obtain a local expression where the left- and right-moving components of the energy density are associated with different weight functions. The results are then compared to numerical calculations for the hopping chain, which requires to consider a proper continuum limit of the lattice entanglement Hamiltonian, obtaining a good agreement with the field-theory prediction.