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 (5)

• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Implementation of Spin Hamiltonians in Optical Lattices
• 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

Cited by in corpus (13)

• Correlation functions and excitation spectrum of the frustrated ferromagnetic spin-1/2 chain in an external magnetic field
• Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Microscopic origin of isotropic non-Heisenberg behavior in highly correlated systems
• Quantum State Transfer in Spin-1 Chains
• Quantum spin nematics, dimerization, and deconfined criticality in quasi-one dimensional spin-1 magnets
• The SU(3) bosons and the spin nematic state on the spin-1 bilinear-biquadratic triangular lattice
• Spontaneous trimerization in a bilinear-biquadratic S=1 zig-zag chain
• Frustration Induced Quantum Phases in Mixed Spin Chain with Frustrated Side Chains
• DMRG Simulation of the SU(3) AFM Heisenberg Model
• Exact models for trimerization and tetramerization in spin chains
• Theory of spin nematic to spin-Peierls quantum phase transition in ultracold spin-1 atoms in optical lattices
• Highest weight state description of the isotropic spin-1 chain