Recent theoretical studies raised the possibility of a realization of spin nematic states in the $S=1$ triangular lattice compound ${\mathrm{NiGa}}_{2}{\mathrm{S}}_{4}$ . 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.Recent theoretical studies raised the possibility of a realization of spin nematic states in the $S=1$ triangular lattice compound ${\mathrm{NiGa}}_{2}{\mathrm{S}}_{4}$. 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.

arXiv:0707.1195Physical Review BDec 12, 200732 citations

Entanglement Entropy in Quantum Spin Chains with Finite Range Interaction

Alexander Rudol'fovich Its, Francesco Mezzadri, M. Y. Mo

arXiv:0708.0161Communications in Mathematical PhysicsAug 11, 200847 citations

Magnetization plateaus in dimerized spin-ladder arrays

D. C. Cabra, Marcelo D. Grynberg

We investigate the ground-state magnetization plateaus appearing in spin- $\frac{1}{2}$ two-leg ladders built up from dimerized antiferromagnetic Heisenberg chains and dimerized zig-zag interchain couplings. Using both Abelian bosonization and Lanczos methods we find that the system yields rather unusual plateaus and exhibits massive and massless phases for specific choices or ``tuning'' of exchange interactions. The relevance of this behavior in the study of ${\mathrm{NH}}_{4}{\mathrm{CuCl}}_{3}$ is discussed.We investigate the ground-state magnetization plateaus appearing in spin-$\frac{1}{2}$ two-leg ladders built up from dimerized antiferromagnetic Heisenberg chains and dimerized zig-zag interchain couplings. Using both Abelian bosonization and Lanczos methods we find that the system yields rather unusual plateaus and exhibits massive and massless phases for specific choices or ``tuning'' of exchange interactions. The relevance of this behavior in the study of ${\mathrm{NH}}_{4}{\mathrm{CuCl}}_{3}$ is discussed.

arXiv:cond-mat/9911387Physical review. B, Condensed matterJul 1, 200015 citations

Entanglement Entropy in Gapped Quantum Spin Chains

Hosho Katsura, Takaaki Hirano, Yasuhiro Hatsugai

Bulletin of the American Physical SocietyMar 8, 20070 citations

Recent theoretical studies raised the possibility of a realization of spin nematic states in the

S=1

triangular lattice compound

{\mathrm{NiGa}}_{2}{\mathrm{S}}_{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.

We investigate the ground-state magnetization plateaus appearing in spin-

\frac{1}{2}

two-leg ladders built up from dimerized antiferromagnetic Heisenberg chains and dimerized zig-zag interchain couplings. Using both Abelian bosonization and Lanczos methods we find that the system yields rather unusual plateaus and exhibits massive and massless phases for specific choices or ``tuning'' of exchange interactions. The relevance of this behavior in the study of

{\mathrm{NH}}_{4}{\mathrm{CuCl}}_{3}

is discussed.