We use the stochastic series expansion quantum Monte Carlo method, together with the eigenstate-to-Hamiltonian mapping approach, to map the localized ground states of the disordered two-dimensional Heisenberg model, to excited states of a target Hami
ltonian. The localized nature of the ground state is established by studying the spin stiffness, local entanglement entropy, and local magnetization. This construction allows us to define many body localized states in an energy resolved phase diagram thereby providing concrete numerical evidence for the existence of a many-body localized phase in two dimensions.
We probe the superconducting gap in the zero temperature ground state of an attractively interacting spin-imbalanced two-dimensional Fermi gas with Diffusion Monte Carlo. A condensate fraction at nonzero pair momentum evidences a spatially non-unifor
m superconducting order parameter. Comparison with exact diagonalisation studies confirms that the nonzero condensate fraction across a range of nonzero fermion pair momenta is consistent with non-exclusive pairing between majority and minority fermions, an extension beyond FFLO theory.
