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

2011/11/25 by Belén Paredes, Paredes, Belén
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Gases (cond-mat.quant-gas) #Quantum and electron transport phenomena #Quantum, superfluid, helium dynamics #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.quant-gas #cond-mat.str-el

paper · pdf · doi:10.48550/arxiv.1111.6092

5 pages, 2 figures, added references

openalex publication_date 2011/11/25 · arxiv created 2011/11/29 · arxiv updated 2011/11/30 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

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.

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