Simulating Heisenberg Interactions in the Ising Model with Strong Drive Fields

TL;DR

This paper demonstrates how strong driving fields in an Ising model can be effectively simulated by XXZ-Heisenberg models, enabling more complex quantum simulations using simpler native Ising-based devices.

Contribution

It introduces an effective mapping from driven Ising models to XXZ-Heisenberg models at high field strengths, facilitating advanced quantum simulations.

Findings

Effective XXZ-Heisenberg model reproduces Ising dynamics under strong drive

Specific drive orientations replicate XXX-Heisenberg model behavior

Mappings are valid above a critical driving field set by phase transitions

Abstract

The time-evolution of an Ising model with large driving fields over discrete time intervals is shown to be reproduced by an effective XXZ-Heisenberg model at leading order in the inverse field strength. For specific orientations of the drive field, the dynamics of the XXX-Heisenberg model is reproduced. These approximate equivalences, valid above a critical driving field strength set by dynamical phase transitions in the Ising model, are expected to enable quantum devices that natively evolve qubits according to the Ising model to simulate more complex systems.