John Chalker

Abstract:

© 2018 American Physical Society. We consider periodically driven Anderson insulators. The short-time behavior for weak, monochromatic, uniform electric fields is given by linear response theory and was famously derived by Mott. We go beyond this to consider both long times - which is the physics of Floquet late time states - and strong electric fields. This results in a "phase diagram" in the frequency-field strength plane, in which we identify four distinct regimes. These are a linear response regime dominated by preexisting Mott resonances, which exists provided Floquet saturation is not reached within a period; a nonlinear perturbative regime, which exhibits multiphoton-absorption in response to the field; a near-adiabatic regime, which exhibits a primarily reactive response spread over the entire sample and is insensitive to preexisting resonances; and finally an enhanced dissipative regime.

Abstract:

We solve a minimal model for an ergodic phase in a spatially extended quantum many-body system. The model consists of a chain of sites with nearest-neighbor coupling under Floquet time evolution. Quantum states at each site span a q-dimensional Hilbert space, and time evolution for a pair of sites is generated by a q2 × q2 random unitary matrix. The Floquet operator is specified by a quantum circuit of depth two, in which each site is coupled to its neighbor on one side during the first half of the evolution period and to its neighbor on the other side during the second half of the period. We show how dynamical behavior averaged over realizations of the random matrices can be evaluated using diagrammatic techniques and how this approach leads to exact expressions in the large-q limit. We give results for the spectral form factor, relaxation of local observables, bipartite entanglement growth, and operator spreading.