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A major challenge in the study of strongly correlated electron systems is to establish a firm link between microscopic models and effective field theory. Quite often, this step involves a leap of faith, and/or extensive numerical studies. For fractional quantum Hall model wave functions, there exists - in some cases - a scheme to infer the long distance physics of the state that is both compelling and simple, and leaves very little room for ambiguity. This scheme involves a local parent Hamiltonian for the state, which unambiguously defines a "zero mode space" of elementary excitations, and what’s known as a "generalized Pauli principle", which efficiently organizes the zero mode space through one-dimensional patterns satisfying local rules. Where this works, universal properties of the state unambiguously emerge from counting exercises in terms of these patterns, which efficiently encode degeneracies, quasi-particle types and charges, and which completely determine an edge conformal field theory. There is even a natural scheme to infer braiding statistics directly, for both Abelian and non-Abelian states. Unfortunately, such a framework thus far exists for some quantum Hall states but not for others. In this talk, I will review the state of the art of this formalism, give reasons of why its "plain vanilla form" is insufficient to describe some important fractional quantum Hall states (e.g., Jain states), and explain how to address this deficiency through a new, more general concept, called "entangled Pauli principles". It will turn out that for some interesting quantum Hall states, the efficient description advertised here involves simple matrix-product-type entanglement. [1] arXiv:1803.00975

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Alexander Seidel, Washington University in Saint Louis
Seminar Room 0.03, ETP
Contact: Achim Rosch