Quantum Café: Topological Order in Quantum Matter

Ideas on topological order have played a prominent role in studies of states of quantum matter with an energy gap: e.g. spin liquid insulators and fractional quantum Hall liquids. However these ideas can also be important in gapless states, including in metals found in numerous correlated electron compounds. I will present simple models of metals with topological order, and compare some results with numerical studies of the Hubbard model on the square lattice.