Tunable Superdiffusion in Integrable Spin Chains Using Correlated Initial States.

Although integrable spin chains host only ballistically propagating particles, they can still feature diffusive charge transfer. This diffusive charge transfer originates from quasiparticle charge fluctuations inherited from the initial state's magnetization Gaussian fluctuations. We show that ensembles of initial states with quasi-long-range correlations lead to superdiffusive charge transfer with a tunable dynamical exponent. We substantiate our prediction with numerical simulations and discuss how finite time and finite size effects might cause deviations.

Quantized Floquet Topology with Temporal Noise.

Time-periodic (Floquet) drive is a powerful method to engineer quantum phases of matter, including fundamentally nonequilibrium states that are impossible in static Hamiltonian systems. One characteristic example is the anomalous Floquet insulator, which exhibits topologically quantized chiral edge states similar to a Chern insulator, yet is amenable to bulk localization. We study the response of this topological system to time-dependent noise, which breaks the topologically protecting Floquet symmetry. Surprisingly, we find that the quantized response, given by partially filling the fermionic system and measuring charge pumped per cycle, remains quantized up to finite noise amplitude. We trace this robust topology to an interplay between diffusion and Pauli blocking of edge state decay, which we expect should be robust against interactions. We determine the boundaries of the topological phase for a system with spatial disorder numerically through level statistics, and corroborate our results in the limit of vanishing disorder through an analytical Floquet superoperator approach. This approach suggests an interpretation of the state of the system as a non-Hermitian Floquet topological phase. We comment on quantization of other topological responses in the absence of Floquet symmetry and potential experimental realizations.

Topological Floquet-Thouless Energy Pump.

We explore adiabatic pumping in the presence of a periodic drive, finding a new phase in which the topologically quantized pumped quantity is energy rather than charge. The topological invariant is given by the winding number of the micromotion with respect to time within each cycle, momentum, and adiabatic tuning parameter. We show numerically that this pump is highly robust against both disorder and interactions, breaking down at large values of either in a manner identical to the Thouless charge pump. Finally, we suggest experimental protocols for measuring this phenomenon.