Semionic resonating valence bond states

Abstract

The nature of the kagome Heisenberg antiferromagnet (HAFM) is under ongoing debate. While recent evidence points towards a Z_2 topological spin liquid, the exact nature of the topological phase is still unclear. In this paper, we introduce semionic Resonating Valence Bond (RVB) states, this is, Resonating Valence Bond states which are in the Z_2 ordered double-semion phase, and study them using Projected Entangled Pair States (PEPS). We investigate their physics and study their suitability as an ansatz for the HAFM, as compared to a conventional RVB state which is in the Toric Code Z_2 topological phase. In particular, we find that a suitably optimized "semionic simplex RVB" outperforms the equally optimized conventional "simplex RVB" state, and that the entanglement spectrum (ES) of the semionic RVB behaves very differently from the ES of the conventional RVB, which suggests to use the ES to discriminate the two phases. Finally, we also discuss the possible relevance of space group symmetry breaking in valence bond wavefunctions with double-semion topological order.

14 pages, 21 figures. v2: minor corrections

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• Fault-tolerant quantum computation by anyons
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
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• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• An RVB phase in the triangular lattice quantum dimer model
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• Resonating valence bond states in the PEPS formalism
• Explicit tensor network representation for the ground states of string-net models
• Topological and Entanglement Properties of Resonating Valence Bond wavefunctions
• Constructing gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice
• Topological order in PEPS: Transfer operator and boundary Hamiltonians
• Simplex Z_2 spin liquids on the Kagome lattice with Entangled Pair States: spinon and vison coherence lengths, topological entropy and gapless edge modes
• Linear independence of nearest neighbor valence bond states on the kagome lattice and construction of SU(2)-invariant spin-1/2-Hamiltonian with a Sutherland-Rokhsar-Kivelson quantum liquid ground state
• Competing Valence Bond Crystals in the Kagome Quantum Dimer Model
• Ground state uniqueness of the twelve site RVB spin-liquid parent Hamiltonian on the kagome lattice

Cited by in corpus (16)

• Phase diagram of the J1-J2 Heisenberg model on the kagome lattice
• Entanglement Entropy From Tensor Network States for Stabilizer Codes
• Constraints on topological order in Mott Insulators
• Symmetric tensor networks and practical simulation algorithms to sharply identify classes of quantum phases distinguishable by short-range physics
• Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids
• Ising Anyons in Frustration-Free Majorana-Dimer Models
• Evidence for deconfined $U(1)$ gauge theory at the transition between toric code and double semion
• Study of anyon condensation and topological phase transitions from a ${\mathbb{Z}}_4$ topological phase using Projected Entangled Pair States
• Double Semion Phase in an Exactly Solvable Quantum Dimer Model on the Kagome Lattice
• Long range order and symmetry breaking in Projected Entangled Pair State models
• Double-semion topological order from exactly solvable quantum dimer models
• Entanglement Entropy and Topological Order in Resonating Valence-Bond Quantum Spin Liquids
• Topological ${\mathbb{Z}}_2$ RVB quantum spin liquid on the ruby lattice
• A gapped SU(3) spin liquid with Z_3 topological order
• Translation-Invariant Parent Hamiltonians of Valence Bond Crystals
• Non-Abelian Anyons in Periodically Driven Abelian Spin Liquids