Simone Warzel: From Haldane Pseudopotentials to Matrix Product States: Mathematical Structures in the Fractional Quantum Hall Effect

par Simone Warzel

vendredi 19 juin 2026, 09:30 → 12:00 Europe/Paris

M7-411 (ENS Lyon)

The fractional quantum Hall effect provides one of the most striking examples of a strongly correlated quantum phase of matter. 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. This connects quantum Hall physics with the tensor-network methods that have become central in modern condensed matter theory.

I will discuss recent mathematical advances concerning the proofs of the exponential clustering and a gap in the entanglement spectrum in a thin cylinder geometry emerging from the iMPS description. I will also review the Haldane pseudopotential framework, which identifies model Hamiltonians whose exact zero-energy ground states are the iMPS, and give an overview of known results and open problems.

(The talk is based on joint works with Severin Schraven, Bruno Nachtergaele, Marius Lemm, and Amanda Young)