Professor Fabian Essler

Abstract:

We demonstrate that nonlinear response functions in many-body systems carry a sharp signature of interactions between gapped low-energy quasiparticles. Such interactions are challenging to deduce from linear response measurements. The signature takes the form of a divergent-in-time contribution to the response – linear in time in the case when quasiparticles propagate ballistically – that is absent for free bosonic excitations. We give a physically transparent semiclassical picture of this singular behaviour. While the semiclassical picture applies to a broad class of systems we benchmark it in two simple models: in the Ising chain using a form-factor expansion, and in a nonintegrable model — the spin-1 AKLT chain — using time-dependent density matrix renormalization group (tDMRG) simulations. We comment on extensions of these results to finite temperatures.

Abstract:

In a recent numerical study by Haldar et al. (Phys. Rev. X 11, 031062) it was shown that signatures of proximate quantum critical points can be observed at early and intermediate times after certain quantum quenches. Said work focused mainly on the case of the axial next-nearest neighbour Ising (ANNNI) model. Here we construct a simple time-dependent mean-field theory that allows us to obtain a quantitatively accurate description of these quenches at short times, which for reasons we explain remains a fair approximation at late times (with some caveats). Our approach provides a simple framework for understanding the reported numerical results as well as fundamental limitations on detecting quantum critical points through quench dynamics. We moreover explain the origin of the peculiar oscillatory behaviour seen in various observables as arising from the formation of a long-lived bound state.