Spontaneous trimerization in a bilinear-biquadratic S=1 zig-zag chain

Abstract

Recent theoretical studies raised the possibility of a realization of spin nematic states in the S=1 triangular lattice compound NiGa_2S_4. We study the bilinear-biquadratic spin 1 chain in a zig-zag geometry by means of the density matrix renormalization group method and exact diagonalization. We present the phase diagram focusing on antiferromagnetic interactions. Adjacent to the known Haldane-double Haldane and the extended critical phase with dominant spin nematic correlations we find a trimerized phase with a nonvanishing energy gap. We discuss results for different order parameters, energy gaps, correlation functions, and the central charge, and make connection to field theoretical predictions for the phase diagram.

5 pages, 6 figures, corrected typos

References in corpus (14)

• The density-matrix renormalization group
• Entanglement Entropy and Quantum Field Theory
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Spin Nematic Phase in S=1 Triangular Antiferromagnets
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Spin nematics in the bilinear-biquadratic S=1 spin chain
• An extended massless phase and the Haldane phase in a spin-1 isotropic antiferromagnetic chain
• Possible ferro-spin nematic order in NiGa2S4
• Octupolar order in the multiple spin exchange model on a triangular lattice
• Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians
• Density matrix renormalisation group study of the correlation function of the bilinear-biquadratic spin-1 chain
• Connectivity transition in the frustrated S=1 chain revisited
• Exact trimer ground states on a spin-1 chain
• SU(N) Self-Dual Sine-Gordon Model and Competing Orders

Cited by in corpus (25)

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• SU(N) magnetism in chains of ultracold alkaline-earth-metal atoms: Mott transitions and quantum correlations
• Dimerized Solids and Resonating Plaquette Order in SU(N)-Dirac Fermions
• Generalization of the Haldane conjecture to SU(3) chains
• DMRG studies of critical SU(N) spin chains
• Spinon confinement and the Haldane gap in SU(n) spin chains
• Phase diagram and continuous pair-unbinding transition of the bilinear-biquadratic S=1 Heisenberg chain in a magnetic field
• Bose Metals and Insulators on Multi-Leg Ladders with Ring Exchange
• Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state
• Haldane limits via Lagrangian embeddings
• Unified Phase Diagram of Antiferromagnetic SU(N) Spin Ladders
• Quantum Critical Spin-2 Chain with Emergent SU(3) Symmetry
• DMRG investigation of constrained models: from quantum dimer and quantum loop ladders to hard-boson and Fibonacci anyon chains
• DMRG Simulation of the SU(3) AFM Heisenberg Model
• Nematic Spin Liquid Phase in a Frustrated Spin-1 System on the Square Lattice
• Phase diagrams and excitations of anisotropic $S=1$ quantum magnets on the triangular lattice
• Commensurate-incommensurate transition in the chiral Ashkin-Teller model
• Density Matrix Renormalization Group Study of Nematicity in Two Dimensions: Application to a Spin-$1$ Bilinear-Biquadratic Model on the Square Lattice
• Exact models for trimerization and tetramerization in spin chains
• High temperature non-collinear magnetism in a classical bilinear-biquadratic Heisenberg model
• Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain
• Stabilization of the chiral phase of the SU($6m$) Heisenberg model on the honeycomb lattice with $m$ particles per site for $m$ larger than 1
• Spontaneous time-reversal symmetry breaking without magnetism in a $S=1$ chain
• Fragility of the nematic spin liquid induced by diagonal couplings in the square-lattice SU(3) model