# Emergence of entanglement with temperature and time in factorization-surface states

## TL;DR

This paper investigates how entanglement in quantum many-body systems, specifically in the anisotropic XY model, can emerge or revive with temperature and time, even from initially factorized states with no entanglement.

## Contribution

It demonstrates the revival and generation of entanglement at finite temperatures and during non-equilibrium dynamics in quantum spin chains, highlighting new ways to create entanglement.

## Key findings

- Entanglement revives at factorization points with increasing temperature.
- Significant entanglement is generated during unitary evolution from initially unentangled states.
- External heat baths can induce entanglement between spin pairs through repeated quantum interactions.

## Abstract

There exist zero-temperature states in quantum many-body systems that are fully factorized, thereby possessing vanishing entanglement, and hence being of no use as resource in quantum information processing tasks. Such states can become useful for quantum protocols when the temperature of the system is increased, and when the system is allowed to evolve under either the influence of an external environment, or a closed unitary evolution driven by its own Hamiltonian due to a sudden change in the system parameters. Using the one-dimensional anisotropic XY model in a uniform and an alternating transverse magnetic field, we show that entanglement of the thermal states, corresponding to the factorization points in the space of the system parameters, revives once or twice with increasing temperature. We also study the closed unitary evolution of the quantum spin chain driven out of equilibrium when the external magnetic fields are turned off, and show that considerable entanglement is generated during the dynamics, when the initial state has vanishing entanglement. Interestingly, we find that creation of entanglement for a pair of spins is possible when the system is made open to an external heat bath, interacting through that spin-pair having a repetitive quantum interaction.