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

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.

6 pages, 4 figures, (+ 5 pages, 7 figures)