# Bipartite entanglement entropy of the excited states of the free fermions and the harmonic oscillators

## TL;DR

This paper investigates the entanglement properties of excited states in one-dimensional free fermions and harmonic oscillators, revealing conformal field theory descriptions and universal entanglement behaviors, with implications for experiments and related spin chains.

## Contribution

It demonstrates that excited states of these systems can be described by conformal field theories and introduces a method to measure universal average entanglement entropy experimentally.

## Key findings

- Excited states exhibit conformal field theory characteristics regardless of the gap.
- Even gapless Hamiltonians can have excited states with area-law entanglement due to spectral degeneracy.
- A duality-based method is proposed for experimental measurement of universal average entanglement entropy.

## Abstract

We study general entanglement properties of the excited states of the one dimensional translational invariant free fermions and coupled harmonic oscillators. In particular, using the integrals of motion, we prove that these Hamiltonians independent of the gap (mass) has infinite excited states that can be described by conformal field theories with integer or half-integer central charges. In the case of free fermions, we also show that because of the huge degeneracy in the spectrum, even a gapless Hamiltonian can have excited states with an area-law. Finally, we study the universal average entanglement entropy over eigenstates of the Hamiltonian of the free fermions introduced recently in L. Vidmar, et al., Phys. Rev. Lett. 119, 020601 (2017) https://link.aps.org/doi/10.1103/PhysRevLett.119.020601 . In particular, using a duality relation, we propose a method which can be useful for experimental measurement of the universal average entanglement entropy. Part of our conclusions can be extended to the quantum spin chains that are associated with the free fermions via Jordan-Wigner(JW) transformation.