Modeling the Stability of Topological Matter in Optical Lattices
Final rept. 20 Jul 2012 - 19 Apr 2013
VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG DEPT OF PHYSICS
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The goal of this proposal is to model the stability of quantum states of matter derived from topological insulators against two types of corrections strong inter-particle interactions and heating. I will examine interacting atoms in square optical lattices with spin orbit coupling, and more generally, gauge fields, as a route to building Hubbard models hosting fractional topological insulators. I will analyze these models by combining numerical exact diagonalization on small lattice clusters with an analytic variational theory. I also propose to study a new model of finite temperature topological superconductors of dipoles placed in an optical lattice. I will construct and analyze a model using a combination of mean field theory and quantum Monte Carlo. The proposed work will foster new directions in experiments with optical lattices containing cold atomic gases. These new states of matter should exhibit new particles as excitations. Analyses of the stability of these new topological phases will thus play a crucial role in advancing fundamentally new directions in physics.
- Theoretical Mathematics