QuICS Special Seminar
Commuting projector models (CPMs) have provided microscopic theories for a host of gauge theories and are the venue for Kitaev’s toric code. An immediate question that arises is whether there exist CPMs for the Hall effect, the discovery of which ignited a revolution in modern condensed matter physics. In fact, a no-go theorem has recently appeared suggesting that no CPM can host a nonzero Hall conductance. In this talk, we present a CPM for just that: U(1) states with nonzero Hall conductance. In the context of quantum computation, this corresponds to a stabilizer code where the degrees of freedom are U(1) rotors and the code is protected not by long-range entanglement, but instead by a U(1) symmetry. We evade the no-go theorem because of the countably infinite number of states per site, and along the way we illuminate certain aspects of the group cohomology approach to topological phases for continuous groups.
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