Spectral Gaps, Incompressibility, and Fragmented Matrix-Product States in a Fractional Quantum Hall System

Spectral Gaps, Incompressibility, and Fragmented Matrix-Product States in a Fractional Quantum Hall System

-
Simone Warzel, Technical University of Munich

Zoom link and password:

https://princeton.zoom.us/j/94384542603?pwd=cGxDdUNmb2pnbExxTW1qemVBbkMwZz09

 

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)