Subdiffusion and Heat Transport in a Tilted Two-Dimensional Fermi-Hubbard System

Abstract

Using quantum gas microscopy we study the late-time effective hydrodynamics of an isolated cold-atom Fermi-Hubbard system subject to an external linear potential (a "tilt"). The tilt is along one of the principal directions of the two-dimensional (2D) square lattice and couples mass transport to local heating through energy conservation. We study transport and thermalization in our system by observing the decay of prepared initial density waves as a function of wavelength λ and tilt strength and find that the associated decay time τ crosses over as the tilt strength is increased from characteristically diffusive to subdiffusive with τ ∝ λ 4 . In order to explain the underlying physics we develop a hydrodynamic model that exhibits this crossover. For strong tilts, the subdiffusive transport rate is set by a thermal diffusivity, which we are thus able to measure as a function of tilt in this regime. We further support our understanding by probing the local inverse temperature of the system at strong tilts, finding good agreement with our theoretical predictions. Finally, we discuss the relation of the strongly tilted limit of our system to recently studied 1D models which may exhibit nonergodic dynamics. arXiv:1909.05848v1 [cond-mat.quant-gas]

Subdiffusion in strongly tilted lattice systems

“…We thank Lei Pan for bringing our attention to the experiment [13]. We thank David A. Huse and Alan Morningstar for helpful dicussions.…”

“…Our analysis here can be directly applied to analyze the strongly tilt limit of the tilted Fermi Hubbard model realized in Ref. [13]. Since the analysis is based on the symmetry of the system and does not depend on the details of the local interaction term, the existence of subdiffusion behavior should be general: It is straightforward to generalize the result into a higher dimension, different lattices with reflection symmetry and different interaction terms that commute with the gauge transformation U.…”

“…In this section, we give arguments for the existence of the subdiffusion for a large class of strongly tilted lattice systems. We assume that (1) the system can be described by a lattice Hamiltonian, which would be specified below; (2) the system is ergodic as observed in the experiment [13]; and (3) the strength of the tilt potential is large enough such that the system is in the prethermal regime.…”

“…We have set the lattice constant a Lattice = 1 and assumed the interactions preserve the local particle number n j ≡ a n j,a = a c † j,a c j,a . For the Fermi-Hubbard case [13], we have a ∈ {↑, ↓} and H int (c † j,a , c j,a ) = U n j,↑ n j,↓ . The last term in (1) presents a tilted potential in the x direction.…”

“…Except for these standard transport experiments, the precise control of the Fermi Hubbard model in optical lattice also paves a new way to study physics in some extreme conditions. In a recent work [13], by applying an additional laser beam, authors realize a linear potential, or tilt, in the two-dimensional (2D) Fermi Hubbard model. This is an analogy of applying a electric field in solid-state systems.…”