How thermalization sets in when integrability is weakly broken
In plain words
When a solvable chain of interacting spins is perturbed slightly, it should eventually thermalize, but how long that takes and through which intermediate states is unclear. Small-system numerics often show slower relaxation than simple perturbation theory predicts.
Precise statement
Take an integrable lattice Hamiltonian $H_0$ (e.g. the XXZ chain) plus a generic local perturbation g V. Determine the thermalization time $\tau(g)$ of local observables and the intermediate quasi-stationary state (a deformed generalized Gibbs ensemble) in the limit $L \to \infty$ taken before $g \to 0$, and explain any departure from the Fermi golden rule scaling $\tau \sim g^{-2}$. An answer is a controlled kinetic theory that predicts $\tau(g)$ and the prethermal state for given $H_0$ and $V$, checked against large-scale numerics.
What would settle it
Large-system numerics (tensor networks or quantum simulation) of $\tau(g)$ over at least a decade in $g$, matched by a kinetic theory derived from $H_{0}$ and $V$.
Related problems
- More general than Does the relaxation rate scale as $g^{2}$ in the thermodynamic limit