Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization

Abstract

We search for short-range Hamiltonians of finite spin-1 kagome systems, maximizing the overlaps with lattice Moore-Read states. Our starting point is an exact, long-range parent Hamiltonian for such a state on a finite plane, obtained from conformal field theory. A truncation procedure is applied to it, which retains only short-range terms and makes it easy to define the Hamiltonian on a torus. Finally, the remaining coefficients are optimized, to yield maximized overlaps between exact diagonalization results and model ground states. In the best cases, these overlaps exceed 0.9 and 0.8 for the three lowest states of 12- and 18-site systems, respectively, suggesting that the obtained Hamiltonians are good parent Hamiltonians for a non-Abelian topological order.

This is the final version published in PRB. Some changes (incl. a new section) were made to clarify the presentation and discuss the relation to other works. During the review process, we realized that (6) and (11) are equivalent to the wavefunction and the Hamiltonian (respectively) from [44], which influenced the discussion but not the results. Typos and minor mistakes were corrected

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• High temperature fractional quantum Hall states
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• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Anyonic interferometry and protected memories in atomic spin lattices
• Fractional charge and fractional statistics in the quantum Hall effects
• Optical lattice quantum Hall effect
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• Anyons in Quantum Hall Interferometry
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Truncation of lattice fractional quantum Hall Hamiltonians derived from conformal field theory
• Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus

Cited by in corpus (4)

• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Efficient conversion from fermionic Gaussian states to matrix product states
• Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids