Mathematics Colloquia and Seminars

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Description

Ever since Laughlin’s proposal, the correlation structure inherent in fractional quantum Hall wavefunctions and their relation to the Coulomb gas have been of continued interest. One way to grasp this structure is through an infinite-matrix-product (iMPS) description of such wavefunctions in terms of correlators of a chiral quantum field theory. In this talk, I will present a novel, rigorous version of an iMPS for the full class of Laughlin wavefunctions times an arbitrary symmetric polynomial. I will discuss how this representation renders properties such as factorization inherent in such fractional quantum Hall wavefunctions transparent. Most noteworthy from the analytical point of view, I will present bounds on the correlators of the chiral quantum field theory and explain how to utilize this representation to demonstrate the exponential decay of connected correlations and a gap in the entanglement spectrum on a thin cylinder. (Based on joint work with Severin Schraven.)