We study the response of an isolated quantum system governed by Hamiltonian drawn from Gaussian Rosenzweig-Porter random matrix ensemble to a perturbation controlled small parameter. focus on density states, local states and eigenfunction amplitude overlap correlation functions which are calculated exactly using mapping supersymmetric nonlinear sigma model. show that susceptibility fidelity par...

The many-body localised (MBL) to thermal crossover observed in exact diagonalisation studies remains poorly understood as the accessible system sizes are too small be an asymptotic scaling regime. We develop a model of short 1D chains which MBL phase is destabilised by formation resonances. reproduces several properties numerically crossover, including apparent correlation length exponent $\nu=...