# Lattice Unruh effect and world-line entanglement for the XXZ chain

## TL;DR

This paper explores the lattice Unruh effect in the XXZ chain, linking it to ground-state entanglement and proposing a detector analogue for thermalized entanglement spectrum, supported by quantum Monte Carlo simulations.

## Contribution

It introduces a lattice version of the Unruh effect in the XXZ chain and connects it to entanglement, providing a new interpretative framework and a detector analogue.

## Key findings

- Lattice Unruh temperature is related to anisotropy parameter and effective acceleration.
- Quantum Monte Carlo simulations support the connection between world lines and entanglement.
- Proposes an XXZ-chain analogue of a detector for thermalized entanglement spectrum.

## Abstract

For the XXZ chain, we discuss the relation between a lattice version of Unruh effect and the ground-state entanglement on the basis of the corner Hamiltonian. We find that the lattice Unruh temperature is interpreted as $\beta_\lambda = 2\pi/a$ with an effective acceleration $a=\pi/\lambda$, where $\lambda$ denotes the anisotropy parameter of the XXZ chain. Using quantum Monte Carlo simulation for the corner Hamiltonian at $\beta_\lambda$, we demonstrate that world lines of spins surrounding the entangle point provides an intuitive understanding the quantum entanglement. We also propose an XXZ-chain analogue of the detector for the thermalized entanglement spectrum with use of the angular time evolution defined by the corner Hamiltonian.