Topological ${\mathbb{Z}}_2$ Resonating-Valence-Bond Spin Liquid on the Square Lattice

Abstract

A one-parameter family of long-range resonating valence bond (RVB) state on the square lattice was previously proposed to describe a critical spin liquid (SL) phase of the spin-$1/2$ frustrated Heisenberg model. We provide evidence that this RVB state in fact also realises a topological (long-range entangled) ${\mathbb{Z}}_2$ SL, limited by two transitions to critical SL phases. The topological phase is naturally connected to the ${\mathbb{Z}}_2$ gauge symmetry of the local tensor. This work shows that, on one hand, spin-$1/2$ topological SL with $C_{4v}$ point group symmetry and $SU(2)$ spin rotation symmetry exists on the square lattice and, on the other hand, criticality and nonbipartiteness are compatible. We also point out that, strong similarities between our phase diagram and the ones of classical interacting dimer models suggest both can be described by similar Kosterlitz-Thouless transitions. This scenario is further supported by the analysis of the one-dimensional boundary state.

v2: improve presentation, present new evidence and add references

References in corpus (8)

• Criticality, the area law, and the computational power of PEPS
• Resonating valence bond states in the PEPS formalism
• Interacting classical dimers on the square lattice
• Classical dimers with aligning interactions on the square lattice
• Quantum critical phase with infinite projected entangled paired states
• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• Critical Correlations for Short-Range Valence-Bond Wave Functions on the Square Lattice
• Criticality of a classical dimer model on the triangular lattice

Cited by in corpus (20)

• SU$(3{)}_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS
• Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks
• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• Quantum spin liquid phase in the Shastry-Sutherland model detected by an improved level spectroscopic method
• Detecting a $Z_2$ topologically ordered phase from unbiased infinite projected entangled-pair state simulations
• Topological fracton quantum phase transitions by tuning exact tensor network states
• Interplay of $SU(2)$, point group and translation symmetry for PEPS: application to a chiral spin liquid
• Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice
• Topological ${\mathbb{Z}}_2$ RVB quantum spin liquid on the ruby lattice
• iPEPS study of spin symmetry in the doped $t$-$J$ model
• Gapped $Z_2$ spin liquid in the breathing kagome Heisenberg antiferromagnet
• SU(3) trimer resonating-valence-bond state on the square lattice
• Real-time dynamics of a critical Resonating Valence Bond spin liquid
• SU(4) topological RVB spin liquid on the square lattice
• Quantum state preparation of topological chiral spin liquids via Floquet engineering
• Chiral spin liquids with projected Gaussian fermionic entangled pair states
• Discrete lattice symmetry breaking in a two-dimensional frustrated spin-1 Heisenberg model
• Tensor network variational optimizations for real-time dynamics: application to the time-evolution of spin liquids
• Robustness of critical U(1) spin liquids and emergent symmetries in tensor networks
• Triplet resonating valence bond theory and transition metal chalcogenides