Quantum Phase Transition between Z2 spin liquid and columnar Valence Bond Crystals on a Triangular lattice

Abstract

We study the quantum phase transition between the $Z_2$ spin liquid and valence bond solid (VBS) orders on a triangular lattice. With a fully isotropic triangular lattice, the transition from a columnar or resonating-plaquette VBS order can be either first order or there could be two transitions with an intermediate phase. If the transition splits into two, then the $Z_2$ spin liquid will first experience a first order $q=3$ Potts transition to a new nematic $Z_2$ spin liquid that breaks the $2\pi /3$ lattice rotation symmetry (but retain translation symmetry unlike the VBS states). The second transition will then take this new nematic $Z_2$ spin liquid to a columnar or resonating-plaquette VBS state through a second order $3d$ XY${}^{\ast }$ transition. On a distorted triangular lattice, the degeneracy between some of the different columnar VBS orders is lifted, and the phase transition can reduce to a single $3d$ XY${}^{\ast }$ transition.

7 pages, 4 figures

References in corpus (13)

• Magnetic Order versus superconductivity in the Iron-based layered La(O1-xFx)FeAs systems
• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Theory of Electron Nematic Order in LaOFeAs
• Identifying Topological Order by Entanglement Entropy
• Ising and Spin orders in Iron-based Superconductors
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States
• Emergence of inhomogeneous moments from spin liquid in the triangular-lattice Mott insulator $\kappa$-(ET)${}_2$Cu${}_2$(CN)${}_3$
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
• Universal Signatures of Fractionalized Quantum Critical Points
• Unconventional Quantum Critical Points
• Quantum Dimer Model on the triangular lattice: Semiclassical and variational approaches to vison dispersion and condensation

Cited by in corpus (14)

• Spin liquid nature in the Heisenberg $J_1$-$J_2$ triangular antiferromagnet
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• Competing Spin Liquid States in the Spin-$1/2$ Heisenberg Model On Triangular Lattice
• Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4
• Frustration and quantum criticality
• Symmetric $Z_2$ spin liquids and their neighboring phases on triangular lattice
• Detection and characterization of symmetry-broken long-range orders in the spin-$\frac{1}{2}$ triangular Heisenberg model
• Metal-Insulator Transition with Charge Fractionalization
• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Existence of two distinct valence bond solid states in the dimerized frustrated ferromagnetic $J_1$-$J_1^{\prime }$-$J_2$ chain
• Deconfined criticality as intrinsically gapless topological state in one dimension
• $Z_3$ topological order in the quantum dimer-pentamer model
• Sign-problem-free effective models of triangular lattice quantum antiferromagnets
• Vison condensation and spinon confinement in a kagome-lattice ${\mathbb{Z}}_2$ spin liquid: A numerical study of a quantum dimer model