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Bridging partons and coupled-wire approaches to strongly entangled quantum matter

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The Hallmark of strongly entangled quantum phases is an intrinsic impossibility to describe them locally in terms of microscopic degrees of freedom. Two popular methods that have been developed to analytically describe these exotic states are known as (1) ‘parton construction’ and (2) ‘coupled-wire approach’. The former provides a constructive route for determining which non-trivial phases may arise, in principle, for a given set of constituent degrees of freedom and symmetries. This capability comes at the expense of having very little predictive power what phases do arise, in practice, in any particular system. The latter technique, by contrast, yields explicit expressions of ground states, excitations as well as parent Hamiltonians in terms of microscopic degrees of freedom. The price to pay is a lack of flexibility, and each phase needs to be analyzed on a laborious case-by-case basis. I will show how recent understanding of two-dimensional dualities provides a natural link between the two approaches. Specifically, I will show how a wide range of parton mean-field states can be easily translated into explicit coupled-wire models, and how their universal properties can be obtained in a transparent manner.