Quantum Ising model on two dimensional anti-de Sitter space

TL;DR

This paper explores the quantum Ising model on discretized two-dimensional anti-de Sitter space, using classical and quantum algorithms to study thermalization and information scrambling, revealing regimes with unique thermalization behaviors.

Contribution

It introduces a novel study of the quantum Ising model on AdS space, comparing classical and quantum simulation methods for real-time dynamics and thermalization properties.

Findings

Thermalization time can depend logarithmically on system size.

Different regimes of thermalization are observed based on space curvature.

Quantum and classical simulations show consistent results in certain regimes.

Abstract

This paper investigates the transverse Ising model on a discretization of two-dimensional anti-de Sitter space. We use classical and quantum algorithms to simulate real-time evolution and measure out-of-time-ordered correlators (OTOC). The latter can probe thermalization and scrambling of quantum information under time evolution. We compared tensor network-based methods both with simulation on gated-based superconducting quantum devices and analog quantum simulation using Rydberg arrays. While studying this system's thermalization properties, we observed different regimes depending on the radius of curvature of the space. In particular, we find a region of parameter space where the thermalization time depends only logarithmically on the number of degrees of freedom.