In the thin cylinder regime Haldane’s pseudo-potential corresponding to one-third filling results in a frustration-free fermionic lattice Hamiltonian which is dipole-conserving with an added electrostatic interaction. Its zero-energy eigenspace is exponentially large. Nevertheless, it admits a a rather simple, full description in terms of a certain class of fragmented matrix-product states, which I will introduce and discuss in this talk.

As I will sketch, the complete classification of zero-energy states can be taken as a basis for a proof of a uniform spectral gap in the excitation spectrum of these Hamiltonians. The latter is vital for the theoretical explanation of the incompressibility of the FQH system at maximal filling.

(Based on the joint work https://arxiv.org/abs/2004.04992 with B. Nachtergaele and A. Young)

Link to the Zoom seminar:

https://princeton.zoom.us/j/94384542603

(Note that an active password is required, and we are giving a hint of what it is)

**Password: Wigne* (complete * so it spells the name of a distinguished mathematical physicist with past PU connection)**