Despite its many successes, linear response has its limitations as a probe of correlated quantum matter. Nonlinear response, and specifically multidimensional coherent spectroscopy (MDCS), provides one way to overcome some of these limitations. MDCS, a staple tool in chemistry and atomic physics of few-body systems, probes higher-order multiple-time correlations of a near-equilibrium system. Experimental efforts are underway to extend this to a probe of both clean  and disordered  many-body systems, but the theoretical toolbox for computing nonlinear response in interacting quantum systems is primitive. In this talk, I will present two classes of problem where (asymptotically) exact calculations of nonlinear response are possible: (i) disordered systems in the asymptotic scaling regime of infinite-randomness fixed points, where MDCS accesses exponents that characterise the critical points and proximate Griffiths phases ; and (ii) interacting integrable systems in one dimension, where generalised hydrodynamics can be leveraged into a formalism to compute multipoint correlators that is exact in the Eulerian hydrodynamic limit, revealing distinctions between free and interacting integrable systems and providing recursive expressions for nonlinear Drude weights .
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