Many-body localisation: a tale of correlations and classical percolation on Fock space

Many-body localised (MBL) phases of matter fall outside the conventional  paradigm of equilibrium statistical mechanics and thermodynamics. A natural question thus is, what minimal and generic properties must random many-body Hamiltonians possess for a localised phase to be stable? In this talk, I will address the question by exploiting the exact mapping between a many-body Hamiltonian and a tight-binding problem on the Fock-space graph. In particular, I will present a  theory for how the strong correlations in the effective Fock-space disorder play a central role in stabilising an MBL phase.  The theory is rooted in analytic but approximate  calculations of the propagators on the Fock space. To shed further light on the underlying physics, I will also introduce and discuss a classical proxy for the MBL transition in the form of a percolation transition on the Fock space.  Finally, I will discuss a novel class of Anderson localisation problems on  correlated trees, to understand the effect of such disorder correlations in a more controlled setting.

References: Phys. Rev. B 101, 134202 (2020);  Phys. Rev. Lett. 125, 250402 (2020);  Phys. Rev. B 99, 220201 (2019);   Phys. Rev. B 99, 104206 (2019).