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 βλ = 2π=a with an effective acceleration a = π=λ, where λ denotes the anisotropy parameter of the XXZ chain. Using quantum Monte Carlo simulation for the corner Hamiltonian at βλ, 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.