Magnetization cusp singularities of frustrated Kondo necklace model

Magnetization processes of frustrated Kondo necklace model are studied by means of a density matrix renormalization group (DMRG) method and an elementary band theory based on a bond-operator formalism. The DMRG calculations clearly show the cusp singularity in a low-magnetization region ($0<m<1/2$) besides that in a high-magnetization region ($1/2<m<1$) which is expected from previous studies on the magnetization curve of the Majumdar-Ghosh model. An appearance mechanism of the low-magnetization cusp is interpreted in terms of a double-well shape of a low-energy band arising from frustrations between nearest- and next-nearest-neighbor interactions. We also discuss critical behaviors of magnetization near the cusp and obtain a phase diagram showing whether the cusp appears in the magnetization curve or not.Comment: 8 pages, 7 figures. to be published in J. Phys. Soc. Jp

Middle-Field Cusp Singularities in the Magnetization Process of One-Dimensional Quantum Antiferromagnets

We study the zero-temperature magnetization process (M-H curve) of one-dimensional quantum antiferromagnets using a variant of the density-matrix renormalization group method. For both the S=1/2 zig-zag spin ladder and the S=1 bilinear-biquadratic chain, we find clear cusp-type singularities in the middle-field region of the M-H curve. These singularities are successfully explained in terms of the double-minimum shape of the energy dispersion of the low-lying excitations. For the S=1/2 zig-zag spin ladder, we find that the cusp formation accompanies the Fermi-liquid to non-Fermi-liquid transition.Comment: 4 pages, RevTeX, 3 figures, some mistakes in references are correcte

Renormalized Harmonic-Oscillator Description of Confined Electron Systems with Inverse-Square Interaction

An integrable model for SU($\nu$) electrons with inverse-square interaction is studied for the system with confining harmonic potential. We develop a new description of the spectrum based on the {\it renormalized harmonic-oscillators} which incorporate interaction effects via the repulsion of energy levels. This approach enables a systematic treatment of the excitation spectrum as well as the ground-state quantities.Comment: RevTex, 7 page

Spectrum of a spin chain with inverse square exchange

The spectrum of a one-dimensional chain of $SU(n)$ spins positioned at the static equilibrium positions of the particles in a corresponding classical Calogero system with an exchange interaction inversely proportional to the square of their distance is studied. As in the translationally invariant Haldane--Shastry model the spectrum is found to exhibit a very simple structure containing highly degenerate ``super-multiplets''. The algebra underlying this structure is identified and several sets of raising and lowering operators are given explicitely. On the basis of this algebra and numerical studies we give the complete spectrum and thermodynamics of the $SU(2)$ system.Comment: 9 pages, late

Delta-Function Bose Gas Picture of S=1 Antiferromagnetic Quantum Spin Chains Near Critical Fields

We study the zero-temperature magnetization curve (M-H curve) of the S=1 bilinear-biquadratic spin chain, whose Hamiltonian is given by $H=\sum_{i} S_i S_{i+1}+\beta (S_iS_{i+1})^2 with$0 \leq \beta <1$. We focus on validity of the delta-function bose-gas picture near the two critical fields: the saturation field$H_s$and the lower critical field$H_c$associated with the Haldane gap. Near$H_s$, we take ``low-energy effective S-matrix'' approach, which gives correct effective bose-gas coupling constant$c$, different from the spin-wave value. Comparing the M-H curve of the bose gas with the product-wavefunction renormalization group (PWFRG) calculation, excellent agreement is seen. Near$H_c$, comparing the PWFRG result with the bose-gas prediction, we find that there are two distinct regions of$\beta$separated by a critical value$\beta_c(\approx 0.41)$. In the region$0<\beta<\beta_c$, the effective coupling$c$is positive but rather small. The small value of$c$makes the ``critical region'' of the square-root behavior$M\sim \sqrt{H-H_c}$very narrow. Further, we find that in the$\beta \to \beta_c-0$, the square-root behavior transmutes to a different one,$M\sim (H-H_c)^{1/4}$. In the region$\beta_c<\beta <1$, the square-root behavior is rather distinct, but the effective coupling$c$ becomes negative.Comment: 6 pages, RevTeX, 8 ps figure

Antiferromagnetic Zigzag Spin Chain in Magnetic Fields at Finite Temperatures

We study thermodynamic behaviors of the antiferromagnetic zigzag spin chain in magnetic fields, using the density-matrix renormalization group method for the quantum transfer matrix. We focus on the thermodynamics of the system near the critical fields in the ground-state magnetization process($M$-$H$ curve): the saturation field, the lower critical field associated with excitation gap, and the field at the middle-field cusp singularity. We calculate magnetization, susceptibility and specific heat of the zigzag chain in magnetic fields at finite temperatures, and then discuss how the calculated quantities reflect the low-lying excitations of the system related with the critical behaviors in the $M$-$H$ curve.Comment: accepted for publication in Physical Review

Invariants of the Haldane-Shastry SU(N)SU(N) Chain

Using a formalism developed by Polychronakos, we explicitly construct a set of invariants of the motion for the Haldane-Shastry $SU(N)$ chain.Comment: 11 pages, UVA-92-0

Novel massless phase of Haldane-gap antiferromagnets in magnetic field

The behavior of Haldane-gap antiferromagnets in strong magnetic field is not universal. While the low-energy physics of the conventional 1D spin-1 Heisenberg model in its magnetized regime is described by one incommensurate soft mode, other systems with somewhat perturbed coupling constants can possess two characteristic soft modes in a certain range of the field strength. Such a {\em two}-component Lutinger liquid phase is realised above the massive Haldane-gap phase, and in general above any massive nonmagnetic phase, when the ground state exhibits short range incommensurate fluctuations already in the absence of the field.Comment: 4 pages, 2 eps figures, to appear in Phys Rev B: Rapid Communication

Fractional S^z excitation and its bound state around the 1/3 plateau of the S=1/2 Ising-like zigzag XXZ chain

We present the microscopic view for the excitations around the 1/3 plateau state of the Ising-like zigzag XXZ chain. We analyze the low-energy excitations around the plateau with the degenerating perturbation theory from the Ising limit, combined with the Bethe-form wave function. We then find that the domain-wall particles carrying $S^z=\pm 1/3$ and its bound state of $S^z=\pm 2/3$ describe well the low-energy excitations around the 1/3 plateau state. The formation of the bound state of the domain-walls clearly provides the microscopic mechanism of the cusp singularities and the even-odd behavior in the magnetization curve.Comment: 13 pages, 15 figure