Relaxation timescales and decay of correlations in a long-range interacting quantum simulator

TL;DR

This paper provides exact analytic results on the dynamics of correlations in long-range quantum Ising models, revealing stretched exponential decay, prethermalization, and potential applications for benchmarking quantum simulators.

Contribution

It offers the first exact solutions for correlation decay in long-range quantum Ising models across arbitrary dimensions, including effects of frustration and prethermalization.

Findings

Correlations decay as stretched or compressed exponentials in time.

Pronounced prethermalization plateaus occur with strong long-range interactions.

Results can be used to benchmark ion-trap quantum simulators.

Abstract

We study the time evolution of correlation functions in long-range interacting quantum Ising models. For a large class of initial conditions, exact analytic results are obtained in arbitrary lattice dimension, both for ferromagnetic and antiferromagnetic coupling, and hence also in the presence of geometric frustration. In contrast to the nearest-neighbour case, we find that correlations decay like stretched or compressed exponentials in time. Provided the long-range character of the interactions is sufficiently strong, pronounced prethermalization plateaus are observed and relaxation timescales are widely separated. Specializing to a triangular lattice in two spatial dimensions, we propose to utilize these results for benchmarking of a recently developed ion-trap based quantum simulator.