Abstract
Dynamical response functions are standard tools for probing local physics near the equilibrium. They provide information about relaxation properties after the equilibrium state is weakly perturbed. In this paper we focus on systems which break the assumption of thermalization by exhibiting persistent temporal oscillations. We provide rigorous bounds on the Fourier components of dynamical response functions in terms of extensive or local dynamical symmetries, i.e., extensive or local operators with periodic time dependence. Additionally, we discuss the effects of spatially inhomogeneous dynamical symmetries. The bounds are explicitly implemented on the example of an interacting Floquet system, specifically in the integrable Trotterization of the Heisenberg XXZ model.
Highlights
Response functions, or susceptibilities, can be used to probe the symmetry breaking phenomena
Ideal conductivity, which is a particular manifestation of ergodicity breaking, can be related to the Drude weight, which corresponds to the zero-frequency behavior of the dynamical response function [2]
Local symmetries can be related to localization phenomena in many-body systems [4,5,6], while extensive symmetries lead to ideal transport at arbitrary temperature and lack of thermalization in integrable models [2, 7,8,9]
Summary
Susceptibilities, can be used to probe the symmetry breaking phenomena. The second class of systems that defy relaxation to equilibrium are quantum time crystals [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32], where time-translation symmetry breaking occurs for typical states, or equivalently, on the level of dynamical response functions [30, 33]. The emergence of time-translation symmetry breaking in strongly interacting systems has recently been related to extensive dynamical symmetries [30], calling for the development of a rigorous framework. We apply our results to a nontrivial example of a many-body Floquet system that breaks the discrete time-translation symmetry, to the integrable Trotterization of the spin-1/2 XXZ model [34, 35]
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