Glassy states in fermionic systems with strong disorder and interactions
We study the competition between interactions and disorder in two dimensions. Whereas a noninteracting system is always Anderson localized by disorder in two dimensions, a pure system can develop a Mott gap for sufficiently strong interactions. Within a simple model, with short-ranged repulsive interactions, we show that, even in the limit of strong interaction, the Mott gap is completely washed out by disorder for an infinite system for dimensions $D\ensuremath{\le}2$, leading to a glassy state. Moreover, the Mott insulator cannot maintain a broken symmetry in the presence of disorder. We then show that the probability of a nonzero gap as a function of system size falls onto a universal curve, reflecting the glassy dynamics. An analytic calculation is also presented in one dimension that provides further insight into the nature of slow dynamics.
This work describes a high order accurate discontinuous finite element method for the numerical solution of the equations governing compressible inviscid flows. Our investigation has focused on the problem of correctly prescribing the boundary conditions along curved boundaries. “Ale show by numerical testing that, in the presence of curved boundaries, a high order approximation of the solution requires a corresponding high-order approximation of the geometry of the domain. Numerical solutions of transonic flows are presented which illustrate the versatility and the accuracy of the proposed method.