Relaxation time of a strongly tilted Fermi-Hubbard chain
In plain words
Atoms in a strongly tilted lattice can move only in ways that keep their centre of mass fixed, which splits their states into disconnected sectors. Weak extra processes slowly connect the sectors, and how slowly is not known.
Precise statement
In a Fermi-Hubbard chain with tunneling $J$, interaction $U$ and potential step $\Delta$ per site ($\Delta >> J, U$, away from resonances $\Delta = n U$), the order-$J^2/\Delta$ effective Hamiltonian conserves dipole moment and is fragmented. Higher-order terms keep dipole conservation (valid up to times exponential in $\Delta/\operatorname{max}(J,U)$) but connect fragments. Determine the decay time $\tau$ of a density-wave imbalance as a function of $\Delta/J$ and $U/J$ as $L \to \infty$, set by these fragment-connecting processes; answer: the scaling form of $\tau$.
What would settle it
An effective-Hamiltonian prediction for $\tau$ compared with quantum-gas microscope experiments and large-scale numerics over a decade of $\Delta/J$.
Status in the literature
Kohlert et al. (PRL 130, 010201, 2023) showed effective fragmented models capture relaxation at moderate tilt, and the earlier claim of disorder-free Stark localization (Schulz et al. 2019) is attributed to this fragmentation (Doggen, Gornyi, Polyakov 2021); the asymptotic large-$\Delta$ scaling is not established.