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arXiv:cond-mat/0005526 · Physical review. B, Condensed matter

Dynamical properties of spin-orbital chains in a magnetic field

Weiqiang Yu, Stephan Haas

Published Dec 20, 2000• 13 citations
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Abstract

The excitation spectrum of the one-dimensional spin-orbital model in a magnetic field is studied, using a recently developed dynamical density-matrix renormalization-group technique. The method is applied to chains with up to 80 sites, and examined for test cases such as the one-dimensional spin-1/2 Heisenberg antiferromagnet whose excitation spectrum is known exactly from the Bethe ansatz. In the spin-orbital chain, the characteristic dynamical response depends strongly on the model parameters and the applied magnetic field. The coupling between the spin and orbital degrees of freedom is found to influence the incommensuration at finite magnetizations. In the regions of the phase diagram with only massive spin and orbital excitations, a finite field is required to overcome the spin gap. An orbital mode is found to become massless in this partially spin-polarized regime, indicating a strong coupling between the two degrees of freedom. In the critical region with three elementary gapless excitations, a prominent particle-hole excitation is observed at higher energies, promoted by the biquadratic term in the model Hamiltonian of the spin-orbital chain.

DOI
10.1103/physrevb.63.024423

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This thesis examines the Heisenberg antiferromagnetic spin chain in one dimension (1D) with a crystal field splitting term and applied magnetic field term. We use theoretical techniques from quantum field theory and conformal field theory (CFT) to make predictions about the excitation spectrum for our model. We then use Density Matrix Renormalization Group (DMRG) numerical techniques to simulate our spin chain and extract the energy spectrum as we vary our crystal field splitting and magnetic field terms. These results are compared and we examine where theoretical calculations accurately describe our system. This work is motivated by recent experimental work done on SrNi₂Vi₂O₈ by Bera et al. [1] which is a quasi-1D material with weakly coupled spin chains in the bulk. These 1D chains are expected to be described by the Hamiltonian we study in this thesis, and we neglect interchain coupling. We first consider our system where the crystal field splitting term is set to zero, which can be described theoretically using a mapping to the non linear sigma model (NLSM). Near the critical field, it undergoes a Bose condensation transition whose excitation spectrum can be mapped to non-interacting fermions in 1D. We then consider large negative crystal field splitting, and find that near small applied magnetic field we can describe some excited states using Landau-Ginsburg theory. Near critical field, we show that the transition is in the Ising universality, and use results from CFT to predict the spectrum for finite size systems. This allows us to make predictions about where the transition field would be for very large or infinite system size. Finally, we examine our crystal field splitting tuned to the value obtained in Ref. 1, which is a small, negative value. We observe qualitative elements in this spectrum from the spectra obtained at zero and large negative crystal field splitting.

•Jan 1, 2017•0 citations
The excitation spectrum of the one-dimensional spin-orbital model in a magnetic field is studied, using a recently developed dynamical density-matrix renormalization-group technique. The method is applied to chains with up to 80 sites, and examined for test cases such as the one-dimensional spin-1/2 Heisenberg antiferromagnet whose excitation spectrum is known exactly from the Bethe ansatz. In the spin-orbital chain, the characteristic dynamical response depends strongly on the model parameters and the applied magnetic field. The coupling between the spin and orbital degrees of freedom is found to influence the incommensuration at finite magnetizations. In the regions of the phase diagram with only massive spin and orbital excitations, a finite field is required to overcome the spin gap. An orbital mode is found to become massless in this partially spin-polarized regime, indicating a strong coupling between the two degrees of freedom. In the critical region with three elementary gapless excitations, a prominent particle-hole excitation is observed at higher energies, promoted by the biquadratic term in the model Hamiltonian of the spin-orbital chain.
The low-energy effective Hamiltonian of three coupled spin chains with periodic boundary conditions (spin tube) is expressed, in the limit of strong interchain coupling, in terms of XXZ\mathrm{XXZ}XXZ chains coupled by biquadratic exchange interaction. A similar effective model was also proposed to describe the coupling of spins to orbital degrees of freedom in materials such as NaV2O5.{\mathrm{NaV}}_{2}{\mathrm{O}}_{5}.NaV2​O5​. We investigate the effective model by means of bosonization and renormalization-group techniques, and find that the generic phase diagram comprises a gapless region and gapped regions consisting of a spin liquid phase and various antiferromagnetic phases. We discuss the properties of the spin liquid phase, in particular the nature of the ground state and of the elementary excitations above it. We then study the effect of a magnetic field, and conclude that a strong enough magnetic field can suppress the dimerized phase leading to a two component Luttinger liquid. The critical exponents at the gapful-gapless transition are calculated and shown to be nonuniversal in the spin-tube case or the generic spin- orbital problem.
The dynamical spin structure factor and the Raman response are calculated for structurally dimerized and spin-Peierls chains in a magnetic field, using exact diagonalization techniques. In both cases there is a spin liquid phase composed of interacting singlet dimers at small fields h<hc1,h<{h}_{c1},h<hc1​, an incommensurate regime (hc1<h<hc2){(h}_{c1}<h<{h}_{c2})(hc1​<h<hc2​) in which the modulation of the triplet excitation spectra adapts to the applied field, and a fully spin-polarized phase above an upper critical field hc2.{h}_{c2}.hc2​. For structurally dimerized chains, the spin gap closes in the incommensurate phase, whereas spin-Peierls chains remain gapped. In the spin liquid regimes, the dominant feature of the triplet spectra is a one-magnon bound state, separated from a continuum of states at higher energies. There are also indications of a singlet bound state above the one-magnon triplet.
By exploiting density-matrix renormalization group techniques, we investigate the spin dynamics of a spin-1/2 one-dimensional J 1 - J 2 XXZ model with competing ferromagnetic J 1 and antiferromagnetic J 2 exchange couplings under applied magnetic fields. Numerical results of spin excitation spectra show that in the field-induced spin quadrupole regime, the longitudinal component has a gapless mode and the transverse component has a gapped mode irrespective of the exchange anisotropy. The excitation gap of the transverse spin excitation increases as the exchange anisotropy increases over the XY-like and Ising-like regions, demonstrating that two-magnon bound states are stabilized due to the easy-axis anisotropy.
We study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum---with low-energy peaks resembling spinonic excitations---already at intermediate on-site repulsion as small as $U/t\ensuremath{\sim}2--3$, although ratios of peak intensities at different momenta continue evolving with increasing U/tU/tU/t converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of U/tU/tU/t of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.
The spin fluctuations parallel to the external magnetic field in the ground state of the one-dimensional (1D) s=12s=\frac{1}{2}s=21​ Heisenberg antiferromagnet are dominated by a two-parameter set of collective excitations. In a cyclic chain of N sites and magnetization 0<Mz<N/2,0<{M}_{z}<N/2,0<Mz​<N/2, the ground state, which contains 2Mz{2M}_{z}2Mz​ spinons, is reconfigured as the physical vacuum for a different species of quasiparticles, identifiable in the framework of the coordinate Bethe ansatz by characteristic configurations of Bethe quantum numbers. The dynamically dominant excitations are found to be scattering states of two such quasiparticles. For $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty},$ these collective excitations form a continuum in $(q,\ensuremath{\omega})$ space with an incommensurate soft mode. Their matrix elements in the dynamic spin structure factor ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ are calculated directly from the Bethe wave functions for finite N. The resulting line- shape predictions for $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ complement the exact results previously derived via algebraic analysis for the exact two-spinon part of ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ in the zero-field limit. They are relevant for neutron-scattering experiments on quasi-1D antiferromagnetic compounds in a strong magnetic field.
This thesis examines the Heisenberg antiferromagnetic spin chain in one dimension (1D) with a crystal field splitting term and applied magnetic field term. We use theoretical techniques from quantum field theory and conformal field theory (CFT) to make predictions about the excitation spectrum for our model. We then use Density Matrix Renormalization Group (DMRG) numerical techniques to simulate our spin chain and extract the energy spectrum as we vary our crystal field splitting and magnetic field terms. These results are compared and we examine where theoretical calculations accurately describe our system. This work is motivated by recent experimental work done on SrNi₂Vi₂O₈ by Bera et al. [1] which is a quasi-1D material with weakly coupled spin chains in the bulk. These 1D chains are expected to be described by the Hamiltonian we study in this thesis, and we neglect interchain coupling. We first consider our system where the crystal field splitting term is set to zero, which can be described theoretically using a mapping to the non linear sigma model (NLSM). Near the critical field, it undergoes a Bose condensation transition whose excitation spectrum can be mapped to non-interacting fermions in 1D. We then consider large negative crystal field splitting, and find that near small applied magnetic field we can describe some excited states using Landau-Ginsburg theory. Near critical field, we show that the transition is in the Ising universality, and use results from CFT to predict the spectrum for finite size systems. This allows us to make predictions about where the transition field would be for very large or infinite system size. Finally, we examine our crystal field splitting tuned to the value obtained in Ref. 1, which is a small, negative value. We observe qualitative elements in this spectrum from the spectra obtained at zero and large negative crystal field splitting.