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 ∝ k 4 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.

Transport in Stark Many Body Localized Systems

“…Note that our data suggests, that for γ 1 the system becomes localized only in the thermodynamic limit. The observed, apparently subdiffusive growth of the MSD for t > t (γ, L), which is consistent with previous experimental [51] and theoretical works [54,[64][65][66], is therefore a finite-size effect, and will not be considered further in this Letter (see however [48]). For γ ≤ 1 our results are not conclusive, since the delocalization time, if it exists here, is very short, and the plateau in the MSD is not clearly visible.…”

“…1), and cannot be easily generalized for finite and modest electric fields where the Stark-MBL transition ostensibly occurs [43,44,48]. The dynamics in both localized and delocalized phases was studied theoretically [43,44,49,50] and experimentally [51][52][53] starting from special initial states. Twodimensional systems are delocalized and show subdiffusive transport [49,51].…”

“…The dynamics in both localized and delocalized phases was studied theoretically [43,44,49,50] and experimentally [51][52][53] starting from special initial states. Twodimensional systems are delocalized and show subdiffusive transport [49,51]. For one-dimensional systems and sufficiently strong electric fields both charge-density wave (CDW) [43,44,52,53] and domain-walls initial states [50] do not appear to melt completely.…”

Hydrodynamics in lattice models with continuous non-Abelian symmetries

“…We first describe fluids with a conserved U(1) charge and dipole moment, whose hydrodynamics was recently formulated in [58]; see also [59][60][61][62]. An instructive cartoon is to start by supposing that there is a local conserved density ρ corresponding to charge, and s i corresponding to local dipole density orthogonal to x i ρ: namely, the total conserved dipole moment can be written as…”

Space-Dependent Symmetries and Fractons

“…Therefore, the system is diffusive but compared to ordinary diffusion where the spatial width of a distribution increases as a square root of time Δx ∼ t 1/2 , the conservation of higher multipole charges slows down the process to Δx ∼ t 1/(n+1) , i.e. it is subdiffusive [87][88][89][90][91][92][93][94].…”