Noncommutative Geometry Seminar

This work is motivated by the study of quantum many-body

systems, such as integer quantum Hall systems, topological insulators and

superconductors. More generally, we try to characterize entangled

quantum states of spins or electrons on an n-dimensional lattice. We may

impose reasonable restrictions: the state is a ground state of some

local Hamiltonian, the entanglement is also local in some sense, etc. If

we consider the special case of weakly interacting fermions, which

includes all examples above, then the corresponding  quantum states are

classified using the KO spectrum. I conjecture that in the more general

setting, there are two particular Omega-spectra:  F for fermionic

systems and  B  for bosonic (or spin) systems. From the known physical

examples, one can infer the topological spaces F_n, B_n  in low dimensions.