Parametric and Universal Thouless Invariants in Matrix Product States

Speaker: Daniel Spiegel (Harvard University)
Series: Isaac Newton Institute Seminar Series
Note: MMBW03 - Structure of entanglement

Thouless pumping is a well-studied topological phenomenon found in quantum spin chains. In a typical Thouless pump, a spin chain protected by a compact symmetry undergoes a periodic evolution in which charge is transported down the chain, with the amount of charge transported each period being a quantized topological invariant, valued in the Pontryagin dual of the symmetry group. Since the system is periodic, it may be regarded as a parametrized family of states with the circle acting as the parameter space. In this talk, I will generalize the Thouless pumping invariant to an invariant for families of injective matrix product states parametrized by an arbitrary topological space , taking values in the first degree Čech cohomology group . Moreover, I will show how any Thouless invariant can be obtained as a pullback of a single universal Čech class on a classifying space for -symmetric injective matrix product states.