# Entanglement Entropy in Excited States of the Quantum Lifshitz Model

## TL;DR

This paper analyzes the entanglement properties of excited states in the quantum Lifshitz model, revealing universal behaviors and introducing entanglement propagator amplitudes that are explicitly calculated and interpreted.

## Contribution

It extends the understanding of entanglement entropy from ground states to excited states in the quantum Lifshitz model using geometrical and topological methods.

## Key findings

- Entanglement entropy for excited states expressed via entanglement propagator amplitudes.
- EPAs are geometrical probabilities that are universal across lattice and continuum models.
- The quantum Lifshitz model allows analytical computation of excited-state entanglement in 2+1 dimensions.

## Abstract

We investigate the entanglement properties of an infinite class of excited states in the quantum Lifshitz model (QLM). The presence of a conformal quantum critical point in the QLM makes it unusually tractable for a model above one spatial dimension, enabling the ground state entanglement entropy for an arbitrary domain to be expressed in terms of geometrical and topological quantities. Here we extend this result to excited states and find that the entanglement can be naturally written in terms of quantities which we dub "entanglement propagator amplitudes" (EPAs). EPAs are geometrical probabilities that we explicitly calculate and interpret. A comparison of lattice and continuum results demonstrates that EPAs are universal. This work shows that the QLM is an example of a 2+1d field theory where the universal behavior of excited-state entanglement may be computed analytically.