Spin Correlations and Topological Entanglement Entropy in a Non-Abelian Spin-1 Spin Liquid

Abstract

We analyze the properties of a non-Abelian spin-1 chiral spin liquid state proposed by Greiter and Thomale [PRL 102, 207203 (2009)] using variational Monte Carlo. In this state the bosonic $\nu =1$ Moore-Read Pfaffian wave function is used to describe a gas of bosonic spin flips on a square lattice with one flux quantum per plaquette. For toroidal geometries there is a three-dimensional space of these states corresponding to the topological degeneracy of the bosonic Moore-Read state on the torus. We show that spin correlations for different states in this space become indistinguishable for large system size. We also calculate the Renyi entanglement entropy for different system partitions to extract the topological entanglement entropy and provide evidence that the topological order of the lattice spin-liquid state is the same as that of the continuum Moore-Read state from which it is constructed.

4 pages and 2 pages supplemental material, submitted to PRL

References in corpus (8)

• Non-Abelian Anyons and Topological Quantum Computation
• Majorana Zero Modes and Topological Quantum Computation
• The ALPS project release 1.3: open source software for strongly correlated systems
• Resonating valence bond states in the PEPS formalism
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models
• Generalizations of Perelomov's identity on the completeness of coherent states

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• Fractional Chiral Hinge Insulator
• Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians
• Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus
• Non-Abelian Statistics in one dimension: topological momentum spacings and SU(2) level $k$ fusion rules
• Non-Abelian topological order with SO(5)${}_1$ chiral edge states