Spin nematic correlations in bilinear-biquadratic S=1 spin chains

Abstract

We present an extensive numerical study of spin quadrupolar correlations in single and coupled bilinear-biquadratic spin one chains, using several methods such as Exact Diagonalization, Density Matrix Renormalization Group and strong coupling series expansions. For the single chain we clarify the dominant correlation function in the enigmatic gapless period-three phase for theta in (pi/4,pi/2), which is of spin quadrupolar nature with a period three spatial structure. Then we revisit the open problem of the possible existence of a ferroquadrupolar phase between the dimerized and the ferromagnetic phases. Although an extended critical region is in principle compatible with the numerical results, a scenario with a huge crossover scale is more plausible. Finally we study the fate of the dimerized phase upon coupling two chains in a ladder geometry. The dimerized phase rapidly vanishes and an extended gapped phase takes over. This gapped phase presumably has dominant short-ranged ferroquadrupolar correlations for theta in (-3pi,4,-pi/2) and -- suprisingly -- seems to be adiabatically connected to the plaquette single solid phase of the Heisenberg S=1 ladder and therefore also with the Haldane phase of isolated chains.

9 pages, 11 figures. supersedes cond-mat/0311082, significantly extended and rewritten

References in corpus (27)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Dimerization and Incommensurate Spiral Spin Correlations in the Zigzag Spin Chain: Analogies to the Kondo Lattice
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Spin-exchange interactions of spin-one bosons in optical lattices: singlet, nematic and dimerized Phases
• Spin Nematic Phase in S=1 Triangular Antiferromagnets
• Implementation of Spin Hamiltonians in Optical Lattices
• Dimer state of spin-1 Bosons in an optical lattice
• An extended massless phase and the Haldane phase in a spin-1 isotropic antiferromagnetic chain
• Phase diagram of spin-1 bosons on one-dimensional lattices
• Possible ferro-spin nematic order in NiGa2S4
• Néel and Spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets
• Effective field theory for S=1 quantum nematic
• Search for the Nondimerized Quantum Nematic Phase in the Spin-1 Chain
• Quadrupolar Order in Isotropic Heisenberg Models with Biquadratic Interaction
• Probable absence of a quadrupolar spin-nematic phase in the bilinear-biquadratic spin-1 chain
• Renormalization algorithm for the calculation of spectra of interacting quantum systems
• Plaquette-singlet solid state and topological hidden order in spin-1 antiferromagnetic Heisenberg ladder
• Density matrix renormalisation group study of the correlation function of the bilinear-biquadratic spin-1 chain
• Semiclassical description of spin ladders
• Unveiling Order behind Complexity: Coexistence of Ferromagnetism and Bose-Einstein Condensation
• Quantum Effects and Broken Symmetries in Frustrated Antiferromagnets
• The spin-1 ladder : A bosonization study
• Exact Results of Dimerization Order Parameter in $SU(n)$ Antiferromagnetic Chains
• Two-dimensional gapless spin liquids in frustrated SU(N) quantum magnets
• Bifurcation at the c=3/2 Takhtajan-Babujian point to the c=1 critical lines
• Low-energy properties of two-leg spin-1 antiferromagnetic ladders with commensurate external fields and their extensions
• Exact trimer ground states on a spin-1 chain

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