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Irreducibly Interacting Topology through a Hubbard hack
Abstract: Topological states are practically interesting because they, in theory, can be made immune to decoherence. The theory of non-interacting topology is now well understood, and hinges on the ability to factor a many-body state into a product of one-body states. When we add interactions, the space of allowed states is exponentially larger and the possible phases are correspondingly more interesting. In particular, interactions allow for the possibility of “irreducibly interacting topological states” – those with no possible non-interacting analogue. These typically host fundamentally new phenomena - the most well-known being the emergent excitations of the fractional quantum hall effect. Unfortunately, understanding, not to mention realizing, these states often requires us to deal with the notoriously difficult Hubbard model. In this talk, I will give a simple overview of a hack which allows us to sidestep some of the difficulties in dealing with the Hubbard model – the Hatsugai-Kohmoto (HK) model. I will review how the HK model gives us a different approach to interacting physics, how it can be applied to the study of irreducibly interacting topological states, and speculate on whether it offers a different starting point to get closer to the vast array of phases that become possible in the presence of interactions.
Student Bio: Dmitry Manning-Coe is a 5th year graduate student working on emergent phenomena in Barry Bradlyn's group.