Exact parent Hamiltonians of bosonic and fermionic Moore–Read states on lattices and local models

2015/05/19 by Ivan Glasser, J. I. Cirac, J. Ignacio Cirac +2 · 42 citations
Physics and Astronomy · #Boson #Fermion #Lattice (music) #Mathematical physics #Physics #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Theoretical physics #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1088/1367-2630/17/8/082001

published in New Journal of Physics 17(8), 082001 (IOP Publishing) · 15 pages, 7 figures

arxiv created 2015/05/19 · openalex publication_date 2015/08/05 · arxiv updated 2015/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We introduce a family of strongly-correlated spin wave functions on arbitrary spin- and spin-1 lattices in one and two dimensions. These states are lattice analogues of Moore–Read states of particles at filling fraction , which are non-Abelian fractional quantum Hall states in 2D. One parameter enables us to perform an interpolation between the continuum limit, where the states become continuum Moore–Read states of bosons (odd q ) and fermions (even q ), and the lattice limit. We show numerical evidence that the topological entanglement entropy stays the same along the interpolation for some of the states we introduce in 2D, which suggests that the topological properties of the lattice states are the same as in the continuum, while the 1D states are critical states. We then derive exact parent Hamiltonians for these states on lattices of arbitrary size. By deforming these parent Hamiltonians, we construct local Hamiltonians that stabilize some of the states we introduce in 1D and in 2D.

Citations

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Cited by

• Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus
• Fractional Quantum Hall Effects