Scale-invariant freezing of entanglement

TL;DR

This paper demonstrates that bipartite entanglement in various one-dimensional quantum spin models can be frozen over time in a scale-invariant manner, robust against temperature, disorder, and noise type, with implications for quantum information propagation.

Contribution

It introduces the concept of scale-invariant entanglement freezing in 1D quantum spin models under local Markovian noise, supported by exact numerical simulations.

Findings

Entanglement freezing is scale-invariant in certain phases.

Freezing duration is robust against temperature and disorder.

Freezing duration varies quadratically with distance from noise source.

Abstract

We show that bipartite entanglement in a one-dimensional quantum spin model undergoing time-evolution under local Markovian environments can be frozen over time. We demonstrate this by using a number of paradigmatic quantum spin models in one dimension, including the anisotropic XY model in the presence of a uniform and an alternating transverse magnetic field (ATXY), the XXZ model, the XYZ model, and the $J_1-J_2$ model involving the next-nearest-neighbor interactions. We show that the length of the freezing interval, for a chosen pair of nearest-neighbor spins, may remain independent of the length of the spin-chain, for example, in paramagnetic phases of the ATXY model, indicating a scale-invariance. Such freezing of entanglement is found to be robust against a change in the environment temperature, presence of disorder in the system, and whether the noise is dissipative, or not dissipative. Moreover, we connect the freezing of entanglement with the propagation of information through a quantum many-body system, as considered in the Lieb-Robinson theorem. We demonstrate that the variation of the freezing duration exhibits a quadratic behavior against the distance of the nearest-neighbor spin-pair from the noise-source, obtained from exact numerical simulations, in contrast to the linear one as predicted by the Lieb-Robinson theorem.