Subdiffusion in strongly tilted lattice systems

Abstract

The quantum dynamics away from equilibrium is of fundamental interest for interacting lattice systems. In this work, we study strongly tilted lattice systems using the effective Hamiltonian derived from the microscopic description. We first give general arguments for the density relaxation rate satisfying 1/τ ∝ k⁴ for a large class of systems, including the tilted Fermi Hubbard model that has been realized in the recent experiment, E. Guardado-Sanchez et al. [Phys. Rev. X 10, 011042 (2020)]. Here k is the wave vector of the density wave. The main ingredients are the emergence of the reflection symmetry and dipole moment conservation to the leading nontrivial order of the large tilted strength. To support our analysis, we then construct a solvable model with large local Hilbert space dimension by coupling sites discribed by the Sachdev-Ye-Kitaev models, where the density response can be computed explicitly. The the tilt strength and the temperature dependence of the subdiffusion constant are also discussed.

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