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Abstract:

We investigate the possibility of engineering dissipatively long-range order that is robust against heating in strongly interacting fermionic systems, relevant for atoms in cavity QED. It was previously shown [Tindall ] that it is possible to stabilize long-range order in a Hubbard model by exploiting a dissipative mechanism in the Lindblad limit, this latter being valid for spectrally unstructured baths. Here, we first show that this mechanism still holds when including additional spin-exchange interactions in the model, that is, for the tUJ model. Moreover, by means of a Redfield approach that goes beyond the Lindblad case, we show how the stability of the engineered state depends crucially on properties of the bath spectral density and discuss the feasibility of those properties in an experiment.

Abstract:

Using artificial dissipation to tame entanglement growth, we chart the emergence of diffusion in a generic interacting lattice model for varying U(1) charge densities. We follow the crossover from ballistic to diffusive transport above a scale set by the scattering length, finding the intuitive result that the diffusion constant scales as $D\propto 1/\mathrm{��}$ at low densities $\mathrm{��}$ . Our numerical approach generalizes the Dissipation-Assisted Operator Evolution algorithm: in the spirit of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, we effectively approximate nonlocal operators by their ensemble averages, rather than discarding them entirely. This greatly reduces the operator entanglement entropy, while still giving accurate predictions for diffusion constants across all density scales. We further construct a minimal model for the transport crossover, yielding charge correlation functions which agree well with our numerical data. Our results clarify the dominant contributions to hydrodynamic correlation functions of conserved densities, and serve as a guide for generalizations to low-temperature transport.