The many-body localised (MBL) to thermal crossover observed in exact
diagonalisation studies remains poorly understood as the accessible system
sizes are too small to be in an asymptotic scaling regime. We develop a model
of the crossover in short 1D chains in which the MBL phase is destabilised by
the formation of many-body resonances. The model reproduces several properties
of the numerically observed crossover, including an apparent correlation length
exponent ν=1, exponential growth of the Thouless time with disorder
strength, linear drift of the critical disorder strength with system size,
scale-free resonances, apparent 1/ω dependence of disorder-averaged
spectral functions, and sub-thermal entanglement entropy of small subsystems.
In the crossover, resonances induced by a local perturbation are rare at
numerically accessible system sizes L which are smaller than a
\emph{resonance length} λ. For L≫λ​, resonances
typically overlap, and this model does not describe the asymptotic transition.
The model further reproduces controversial numerical observations which Refs.
[\v{S}untajs et al, 2019] and [Sels & Polkovnikov, 2020] claimed to be
inconsistent with MBL. We thus argue that the numerics to date is consistent
with a MBL phase in the thermodynamic limit.Comment: 27 pages, 12 figure