Parent Hamiltonian for the non-Abelian chiral spin liquid

Physical Review B (Impact Factor: 3.66). 01/2012; DOI: 10.1103/PhysRevB.89.165125
Source: arXiv

ABSTRACT We construct a parent Hamiltonian for the family of non-Abelian chiral spin
liquids proposed recently by two of us [PRL 102, 207203 (2009)], which includes
the Abelian chiral spin liquid proposed by Kalmeyer and Laughlin, as the
special case S=1/2. As we use a circular disk geometry with an open boundary,
both the annihilation operators we identify and the Hamiltonians we construct
from these are exact only in the thermodynamic limit.

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    ABSTRACT: We propose 1D and 2D lattice wave functions constructed from the SU(n)_1 Wess–Zumino–Witten (WZW) model and derive their parent Hamiltonians. When all spins in the lattice transform under SU(n) fundamental representations, we obtain a two-body Hamiltonian in 1D, including the SU(n) Haldane–Shastry model as a special case. In 2D, we show that the wave function converges to a class of Halperin's multilayer fractional quantum Hall states and belongs to chiral spin liquids. Our result reveals a hidden SU(n) symmetry for this class of Halperin states. When the spins sit on bipartite lattices with alternating fundamental and conjugate representations, we provide numerical evidence that the state in 1D exhibits quantum criticality deviating from the expected behaviors of the SU(n)_1 WZW model, while in 2D they are chiral spin liquids being consistent with the prediction of the SU(n)_1 WZW model.
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    ABSTRACT: We argue that a relatively simple model containing only SU(2)-invariant chiral three-spin interactions on a Kagome lattice of S=1/2 spins can give rise to both a gapped and a gapless quantum spin liquid. Our arguments are rooted in a formulation in terms of network models of edge states and are backed up by a careful numerical analysis. For a uniform choice of chirality on the lattice, we realize the Kalmeyer-Laughlin state, i.e. a gapped spin liquid which is identified as the nu=1/2 bosonic Laughlin state. For staggered chiralities, a gapless spin liquid emerges which exhibits gapless spin excitations along lines in momentum space, a feature that we probe by studying quasi-two-dimensional systems of finite width. We thus provide a single, appealingly simple spin model (i) for what is probably the simplest realization of the Kalmeyer-Laughlin state to date, as well as (ii) for a non-Fermi liquid state with lines of gapless SU(2) spin excitations.

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