Asymptotically exact theory for nonlinear spectroscopy of random quantum magnets

TL;DR

This paper provides an exact theoretical framework for understanding nonlinear spectroscopy responses in disordered quantum magnets near critical points, revealing critical behavior and relaxation dynamics beyond linear response.

Contribution

It introduces exact scaling forms for nonlinear response functions in the 1D random transverse-field Ising model, applicable to higher-dimensional random quantum magnets.

Findings

Exact scaling forms for relaxation time distributions

Nonlinear response reveals critical behavior absent in linear response

Results applicable to generic random quantum magnets in any dimension

Abstract

We study nonlinear response in quantum spin systems {near infinite-randomness critical points}. Nonlinear dynamical probes, such as two-dimensional (2D) coherent spectroscopy, can diagnose the nearly localized character of excitations in such systems. {We present exact results for nonlinear response in the 1D random transverse-field Ising model, from which we extract information about critical behavior that is absent in linear response. Our analysis yields exact scaling forms for the distribution functions of relaxation times that result from realistic channels for dissipation in random magnets}. We argue that our results capture the scaling of relaxation times and nonlinear response in generic random quantum magnets in any spatial dimension.