# Entanglement hamiltonians in 1D free lattice models after a global quantum quench

## TL;DR

This paper investigates how the entanglement Hamiltonian evolves over time after a global quantum quench in 1D free lattice models, revealing insights into entanglement dynamics and spectrum gaps.

## Contribution

It provides a detailed analysis of the temporal evolution of entanglement Hamiltonians and spectra in free lattice models following a global quench, combining numerical and conformal field theory approaches.

## Key findings

- Entanglement spectrum gaps evolve distinctly over time.
- Contours for entanglement entropy are characterized and analyzed.
- Conformal field theory and quasi-particle models explain the entanglement dynamics.

## Abstract

We study the temporal evolution of the entanglement hamiltonian of an interval after a global quantum quenchin free lattice models in one spatial dimension. In a harmonic chain we explore a quench of the frequency parameter. In a chain of free fermions at half filling we consider the evolution of the ground state of a fully dimerised chain through the homogeneous hamiltonian. We focus on critical evolution hamiltonians. The temporal evolutions of the gaps in the entanglement spectrum are analysed. The entanglement hamiltonians in these models are characterised by matrices that provide also contours for the entanglement entropies. The temporal evolution of these contours for the entanglement entropy is studied, also by employing existing conformal field theory results for the semi-infinite line and the quasi-particle picture for the global quench.