Quantum quench in a driven Ising chain

TL;DR

This paper uncovers an exact solution for the dynamics of a driven Ising chain, revealing non-heating behavior and exotic physics possibilities, including realization of E8 symmetry and confirming meson mass ratios.

Contribution

It identifies a hidden integrable structure in a driven Ising chain enabling exact time-evolution calculations and demonstrates non-heating behavior despite the lack of energy conservation.

Findings

Exact time-evolution accessible due to hidden integrability

Model does not heat to infinite temperature despite driving

Numerical confirmation of meson mass ratio as the golden ratio

Abstract

We consider the Ising chain driven by oscillatory transverse magnetic fields. For certain parameter regimes, we reveal a hidden integrable structure in the problem, which allows access to the \textit{exact time-evolution} in this driven quantum system. We compute time-evolved one- and two-point functions following a quench that activates the driving. It is shown that this model does not heat up to infinite temperature, despite the absence of energy conservation, and we further discuss the generalization to a family of driven Hamiltonians that do not suffer heating to infinite temperature, despite the absence of integrability and disorder. The particular model studied in detail also presents a route for realising exotic physics (such as the E8 perturbed conformal field theory) via driving in quantum chains that could otherwise never realise such behaviour. In particular we numerically confirm that the ratio of the meson excitations masses is given by the golden ratio.