Exact Parent Lattice Hamiltonian for One-Dimensional Non-Abelian Fractional Quantum Hall Liquids

TL;DR

This paper introduces a family of exact one-dimensional lattice Hamiltonians for non-Abelian fractional quantum Hall liquids, revealing their structure, ground states, and connections to spin liquids with hidden order.

Contribution

It provides explicit Hamiltonians and ground states for non-Abelian quantum Hall liquids in one dimension, including their relation to spin liquids and resonating valence bond states.

Findings

Exact ground states for non-Abelian fractional quantum Hall liquids identified.

Connection established between quantum Hall states and non-Abelian spin liquids.

Hamiltonians involve long-range tunneling with amplitudes decaying with chord distance.

Abstract

I present a family of one-dimensional time reversal lattice Hamiltonians whose exact ground states are bosonic non-Abelian fractional quantum Hall liquids with well defined total chiral momentum. These Hamiltonians describe k-hard-core bosons and involve long-range tunneling and interaction processes with an amplitude decaying with the chord distance. For k=2 the ground state is a p-wave paired phase corresponding to the Pfaffian quantum Hall state. This family of non-Abelian liquids is shown to be in one-to-one correspondence with a family of non-Abelian spin-k/2 liquids exhibiting hidden non-local order. They are total singlets made out of k indistinguishable Resonating Valence Bond states. The corresponding spin parent Hamiltonians are obtained.