Topology and Criticality in Resonating Affleck-Kennedy-Lieb-Tasaki loop Spin Liquid States

Abstract

We exploit a natural Projected Entangled-Pair State (PEPS) representation for the resonating Affleck-Kennedy-Lieb-Tasaki loop (RAL) state. By taking advantage of PEPS-based analytical and numerical methods, we characterize the RAL states on various two-dimensional lattices. On square and honeycomb lattices, these states are critical since the dimer-dimer correlations decay as a power law. On kagome lattice, the RAL state has exponentially decaying correlation functions, supporting the scenario of a gapped spin liquid. We provide further evidence that the RAL state on the kagome lattice is a ${\mathbb{Z}}_2$ spin liquid, by identifying the four topological sectors and computing the topological entropy. Furthermore, we construct a one-parameter family of PEPS states interpolating between the RAL state and a short-range Resonating Valence Bond state and find a critical point, consistent with the fact that the two states belong to two different phases. We also perform a variational study of the spin-1 kagome Heisenberg model using this one-parameter PEPS.

10 pages, 14 figures, published version

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• Ising Anyons in Frustration-Free Majorana-Dimer Models
• Subsystem symmetry enriched topological order in three dimensions
• Magnetization Process of the Spin-S Kagome-Lattice Heisenberg Antiferromagnet
• A beginner's guide to non-abelian iPEPS for correlated fermions
• The spin-1/2 Kagome XXZ model in a field: competition between lattice nematic and solid orders
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• Heisenberg antiferromagnet on the Husimi lattice
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• Plaquette-triplon analysis of magnetic disorder and order in a trimerized spin-1 Kagomé antiferromagnet
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• Worldsheet matter for electric flux strings
• Non-perturbative linked-cluster expansions for the trimerized ground state of the spin-one Kagome Heisenberg model
• Spontaneous dimerization and moment formation in the Hida model of spin-1 kagomé antiferromagnet
• SU(3) trimer resonating-valence-bond state on the square lattice
• Classification of trivial spin-1 tensor network states on a square lattice
• Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice
• Discrete lattice symmetry breaking in a two-dimensional frustrated spin-1 Heisenberg model
• String order parameters for symmetry fractionalization in an enriched toric code
• Quantum Loop States in Spin-Orbital Models on the Honeycomb Lattice
• Survival of magnetic correlations above ordering temperature in a ferromagnetically ordered classical kagomé magnet: Li9Cr3(P2O7)3(PO4)2
• Topology-driven phase transitions in the classical monomer-dimer-loop model