Incompressible Quantum Liquids and New Conservation Laws

TL;DR

This paper explores Hamiltonians with unique conservation laws, revealing a universal energy degeneracy linked to fractional fillings, and connects these findings to quantum Hall and dimer liquids, advancing understanding of exotic quantum states.

Contribution

It introduces a class of Hamiltonians with combined center-of-mass position and momentum conservation, unifying fractional quantum Hall and quantum dimer liquids.

Findings

Energy spectrum is at least q-fold degenerate at filling p/q.

Hamiltonian captures fractional quantum Hall and quantum dimer liquids.

Relevance to featureless Mott insulators is discussed.

Abstract

In this letter we investigate a class of Hamiltonians which, in addition to the usual center-of-mass (CM) momentum conservation, also have center-of-mass position conservation. We find that regardless of the particle statistics, the energy spectrum is at least q-fold degenerate when the filling factor is $p/q$, where $p$ and $q$ are coprime integers. Interestingly the simplest Hamiltonian respecting this type of symmetry encapsulates two prominent examples of novel states of matter, namely the fractional quantum Hall liquid and the quantum dimer liquid. We discuss the relevance of this class of Hamiltonian to the search for featureless Mott insulators.