Spring 2014

'Gauging' Time Reversal Symmetry in Tensor Network States

Tuesday, April 22nd, 2014 4:30 pm5:30 pm

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It is well know that unitary symmetries can be 'gauged', i.e. defined to act in a local way, which leads to a corresponding gauge field. Gauging, for example, the charge conservation symmetry leads to electromagnetic gauge fields. It is an open question whether an analogous process is possible for time reversal which is an anti-unitary symmetry. Here we discuss a route to gauging time reversal symmetry that applies to gapped quantum ground states. We show how time reversal can be applied locally and also describe time reversal symmetry twists which act as gauge fluxes through nontrivial loops in the system. The procedure is based on the tensor network representation of quantum states which provides a notion of locality for the wave function coefficient. As with unitary symmetries, gauging time reversal provides useful access to the physical properties of the system. We show how topological invariants of certain symmetry protected topological phases in $D=1,2$ are readily extracted using these ideas and also discuss how they help capture a subtle distinction between time reversal symmetric $Z_2$ gauge theories.