Laboratoire de Physique Théorique
Toulouse - UMR 5152

Once thought to destroy localisation completely, we now know that adding interactions into disordered materials can lead to the formation of a many-body localised phase. This phase is characterised by an extensive number of local conserved quantities and a failure to thermalise. Consequently it cannot be described by conventional equilibrium quantum statistical mechanics, and exact numerical methods are restricted to small system sizes. Here, we present a semi-analytic flow equation approach : we employ a continuous unitary transform to diagonalise the Hamiltonian of a gas of interacting spinless fermions, show how local integrals of motion naturally emerge from this method, and go on calculate time evolution and localisation properties in the strongly-disordered regime in both one and two spatial dimensions.