Gutzwiller Approach for Elementary Excitations in $S=1$ Antiferromagnetic Chains

Abstract

In a previous paper [Phys. Rev. B 85,195144 (2012)], variational Monte Carlo method (based on Gutzwiller projected states) was generalized to $S=1$ systems. This method provided very good trial ground states for the gapped phases of $S=1$ bilinear-biquadratic (BLBQ) Heisenberg chain. In the present paper, we extend the approach to study the low-lying elementary excitations in $S=1$ chains. We calculate the one-magnon and two-magnon excitation spectra of the BLBQ Heisenberg chain and the results agree very well with recent data in literature. In our approach, the difference of the excitation spectrum between the Haldane phase and the dimer phase (such as the even/odd size effect) can be understood from their different topology of corresponding mean field theory. We especially study the Takhtajan-Babujian critical point. Despite the fact that the `elementary excitations' are spin-1 magnons which are different from the spin-1/2 spinons in Bethe solution, we show that the excitation spectrum, critical exponent ($\eta =0.74$) and central charge ($c=1.45$) calculated from our theory agree well with Bethe ansatz solution and conformal field theory predictions.

25+, 10 figures

References in corpus (7)

• Implementation of Spin Hamiltonians in Optical Lattices
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Elementary excitations in gapped quantum spin systems
• Paired chiral spin liquid with a Fermi surface in S=1 model on the triangular lattice
• Entanglement Entropy as a Portal to the Physics of Quantum Spin Liquids
• Projected BCS states and spin Hamiltonians for the SO(n)_1 Wess-Zumino-Witten model
• Dynamical Monte Carlo investigation of spin reversals and nonequilibrium magnetization of single-molecule magnets

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• Fractionalization, entanglement, and separation: understanding the collective excitations in a spin-orbital chain
• Non-Abelian Chiral Spin Liquid on the Kagome Lattice
• Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains
• Symmetry-protected topological order identified via Gutzwiller-guided density-matrix-renormalization-group: $\mathrm{SO}(n)$ spin chains
• Low-energy dynamics of the Affleck-Kennedy-Lieb-Tasaki model in the one- and two-triplon basis