Haldane Gap and Hidden Order in the S=2 Antiferromagnetic Quantum Spin Chain

We have investigated Haldane's conjecture for the S=2 isotropic antiferromagnetic quantum spin chain with nearest-neighbor exchange J. Using a density matrix renormalization group algorithm for chains up to L=350 spins, we find in the thermodynamic limit a finite spin gap of Delta = 0.085(5)J and a finite spin-spin correlation length xi = 49(1) lattice spacings. We establish the ground state energy per bond to be E_0=-4.761248(1)J. We show that the ground state has a hidden topological order that is revealed in a nonlocal string correlation function. This means that the physics of the S=2 chain can be captured by a valence-bond solid description. We also observe effective free spin-1 states at the ends of an open S=2 chain.Comment: 6 pages, LaTeX 2.09, 3 PostScript figure

Coupled S=1/2S=1/2 Heisenberg antiferromagnetic chains in an effective staggered field

We present a systematic study of coupled $S=1/2$ Heisenberg antiferromagnetic chains in an effective staggered field. We investigate several effects of the staggered field in the {\em higher} ({\em two or three}) {\em dimensional} spin system analytically. In particular, in the case where the staggered field and the inter-chain interaction compete with each other, we predict, using mean-field theory, a characteristic phase transition. The spin-wave theory predicts that the behavior of the gaps induced by the staggered field is different between the competitive case and the non-competitive case. When the inter-chain interactions are sufficiently weak, we can improve the mean-field phase diagram by using chain mean-field theory and the analytical results of field theories. The ordered phase region predicted by the chain mean-field theory is substantially smaller than that by the mean-field theory.Comment: 13pages, 12figures, to be published in PR

Theory of Low Temperature Electron Spin Resonance in Half-integer Spin Antiferromagnetic Chains

A theory of low temperature (T) electron spin resonance (ESR) in half-integer spin antiferromagnetic chains is developed using field theory methods and avoiding previous approximations. It is compared to experiments on Cu benzoate. Power laws are predicted for the line-width broadening due to various types of anisotropy. At T -> 0, zero width absorption peaks occur in some cases. The second ESR peak in Cu benzoate, observed at T<.76K, is argued not to indicate Neel order as previously claimed, but to correspond to a sine-Gordon "breather" excitation.Comment: 4 pages, REVTEX, 3 PostScript figures embedded in tex

Direct perturbation theory on the shift of Electron Spin Resonance

We formulate a direct and systematic perturbation theory on the shift of the main paramagnetic peak in Electron Spin Resonance, and derive a general expression up to second order. It is applied to one-dimensional XXZ and transverse Ising models in the high field limit, to obtain explicit results including the polarization dependence for arbitrary temperature.Comment: 5 pages (no figures) in REVTE

Exact Analysis of ESR Shift in the Spin-1/2 Heisenberg Antiferromagnetic Chain

A systematic perturbation theory is developed for the ESR shift and is applied to the spin-1/2 Heisenberg chain. Using the Bethe ansatz technique, we exactly analyze the resonance shift in the first order of perturbative expansion with respect to an anisotropic exchange interaction. Exact result for the whole range of temperature and magnetic field, as well as asymptotic behavior in the low-temperature limit are presented. The obtained g-shift strongly depends on magnetic fields at low temperature, showing a significant deviation from the previous classical result.Comment: 4 pages, 3 figures,to be published in Phys. Rev. Let

The Origin of Magnetic Interactions in Ca3Co2O6

We investigate the microscopic origin of the ferromagnetic and antiferromagnetic spin exchange couplings in the quasi one-dimensional cobalt compound Ca3Co2O6. In particular, we establish a local model which stabilizes a ferromagnetic alignment of the S=2 spins on the cobalt sites with trigonal prismatic symmetry, for a sufficiently strong Hund's rule coupling on the cobalt ions. The exchange is mediated through a S=0 cobalt ion at the octahedral sites of the chain structure. We present a strong coupling evaluation of the Heisenberg coupling between the S=2 Co spins on a separate chain. The chains are coupled antiferromagnetically through super-superexchange via short O-O bonds.Comment: 5 Pages, 3 Figures; added anisotropy term in eq. 9; extended discussion of phase transitio

ESR investigation on the Breather mode and the Spinon-Breather dynamical crossover in Cu Benzoate

A new elementary-excitation, the so called "breather excitation", is observed directly by millimeter-submillimeter wave electron spin resonance (ESR) in the Heisenberg quantum spin-chain Cu benzoate, in which a field-induced gap is found recently by specific heat and neutron scattering measurements. Distinct anomalies were found in line width and in resonance field around the "dynamical crossover" regime between the gap-less spinon-regime and the gapped breather-regime. When the temperature becomes sufficiently lower than the energy gap, a new ESR-line with very narrow line-width is found, which is the manifestation of the breather excitation. The non-linear field dependence of the resonance field agrees well with the theoretical formula of the first breather-excitation proposed by Oshikawa and Affleck. The present work establishes experimentally for the first time that a sine-Gordon model is applicable to explain spin dynamics in a S=1/2 Heisenberg spin chain subjected to staggered field even in high fields.Comment: Revtex, 4 pages, 4 figures, submitted to Phys. Rev. Let

A study on correlation effects in two dimensional topological insulators

We investigate correlation effects in two dimensional topological insulators (TI). In the first part, we discuss finite size effects for interacting systems of different sizes in a ribbon geometry. For large systems, there are two pairs of well separated massless modes on both edges. For these systems, we analyze the finite size effects using a standard bosonization approach. For small systems, where the edge states are massive Dirac fermions, we use the inhomogeneous dynamical mean field theory (DMFT) combined with iterative perturbation theory as an impurity solver to study interaction effects. We show that the finite size gap in the edge states is renormalized for weak interactions, which is consistent with a Fermi-liquid picture for small size TIs. In the second part, we investigate phase transitions in finite size TIs at zero temperature focusing on the effects of possible inter-edge Umklapp scattering for the edge states within the inhomogeneous DMFT using the numerical renormalization group. We show that correlation effects are effectively stronger near the edge sites because the coordination number is smaller than in the bulk. Therefore, the localization of the edge states around the edge sites, which is a fundamental property in TIs, is weakened for strong coupling strengths. However, we find no signs for "edge Mott insulating states" and the system stays in the topological insulating state, which is adiabatically connected to the non-interacting state, for all interaction strengths smaller than the critical value. Increasing the interaction further, a nearly homogeneous Mott insulating state is stabilized.Comment: 20 page