Low-complexity eigenstates of a $\nu = 1/3$ fractional quantum Hall system

TL;DR

This paper characterizes the ground state and low-energy excitations of a fractional quantum Hall system at filling factor 1/3, revealing a fragmented structure, a spectral gap, and low-complexity many-body scars.

Contribution

It introduces a new description of the ground state as a sum of exponentially many matrix product states and proves the spectral gap for the model.

Findings

Ground state composed of fragmented matrix product states

Spectral gap established, indicating incompressibility

Identification of low-energy many-body scars with low complexity

Abstract

We identify the the ground-state of a truncated version of Haldane's pseudo-potential Hamiltonian in a thin cylinder geometry as being composed of exponentially many fragmented matrix product states. These states are constructed by lattice tilings and their properties are discussed. We also report on a proof of a spectral gap, which implies the incompressibility of the underlying fractional quantum Hall liquid at maximal filling $\nu = 1/3$. Low-energy excitations and an extensive number of many-body scars at positive energy density, but nevertheless low complexity, are also identified using the concept of tilings.