佐藤 正寛

We study two-component (or pseudo-spin-1/2) Bose or Fermi gases in one<br /> dimension, in which particles are convertible between the components. Through<br /> bosonization and numerical analyses of a simple lattice model, we demonstrate<br /> that, in such gases, a strong intercomponent repulsion induces spontaneous<br /> population imbalance between the components, namely, the ferromagnetism of the<br /> pseudo spins. The imbalanced phase contains gapless charge excitations<br /> characterized as a Tomonaga-Luttinger liquid and gapped spin excitations. We<br /> uncover a crucial effect of the intercomponent particle hopping on the<br /> transition to the imbalanced phase. In the absence of this hopping, the<br /> transition is of first order. At the transition point, the energy spectrum<br /> reveals certain degeneracy indicative of an emergent SU(2) symmetry. With an<br /> infinitesimal intercomponent hopping, the transition becomes of Ising type. We<br /> determine the phase diagram of the model accurately and test the reliability of<br /> the weak-coupling bosonization formalism.

The low-energy dynamical optical response of dimerized and undimerized spin liquid states in a one-dimensional charge transfer Mott insulator is theoretically studied. An exact analysis is given for the low-energy asymptotic behavior using conformal field theory for the undimerized state. In the dimerized state, the infrared absorption due to the bound state of two solitons, i.e., the breather mode, is predicted with an accurate estimate for its oscillator strength, offering a way to detect experimentally the excited singlet state. The effects of external magnetic fields are also discussed.

When a two-dimensional harmonic potential is applied to bosonic cold atoms, the atoms become a cigar shape and the radial energy level is discretized. If the strength of the potential or the total number of atoms is tuned, the atoms can occupy not only the lowest radial band but also higher bands. This paper shows that when both the lowest band and the second lowest doubly-degenerate bands are filled, the repulsive interaction among atoms induces a ground state circulating along the trap axis, in which the Z(2) reflection symmetry is spontaneously broken.

We theoretically study one-dimensional spin-1/2 multiferroic systems. We focus on the chiral ordered phase with gapless excitations that appears under easy-plane anisotropy. The in-plane chirality dynamics contains gapless solitons associated with local flips of the chirality. These excitations contribute to the low-frequency dielectric response through the magnetoelectric coupling.

Recently, it has been shown that spin nematic (quadrupolar) or higher<br /> multipolar correlation functions exhibit a quasi long-range order in the wide<br /> region of the field-induced Tomonaga-Luttinger-liquid (TLL) phase in spin-1/2<br /> zigzag chains. In this paper, we point out that the temperature dependence of<br /> the NMR relaxation rate 1/T_1 in these multipolar TLLs is qualitatively<br /> different from that in more conventional TLLs of one-dimensional quantum<br /> magnets (e.g., the spin-1/2 Heisenberg chain); 1/T_1 decreases with lowering<br /> temperature in multipolar TLL. We also discuss low-energy features in spin<br /> dynamical structure factors which are characteristic of the multipolar TLL<br /> phases.

We investigate quantum phase transitions of the S= 1 2 three-leg antiferromagnetic spin tube with asymmetric interchain (rung) exchange interactions. On the basis of the electron tube system, we propose a useful effective theory to give the global phase diagram of the asymmetric spin tube. In addition, using other effective theories we raise the reliability of the phase diagram. The density-matrix renormalization-group and the numerical diagonalization analyses show that the finite spin gap appears in a narrow region around the rung-symmetric line, in contrast to a recent paper by Nishimoto and Arikawa, [Phys. Rev. B 78, 054421 (2008)]. The numerical calculations indicate that this global phase diagram obtained by use of the effective theories is qualitatively correct. In the gapless phase on the phase diagram, the numerical data are fitted by a finite-size scaling in the c=1 conformal field theory. We argue that all the phase transitions between the gapful and gapless phases belong to the Berezinskii-Kosterlitz-Thouless universality class. © 2008 The American Physical Society.

We theoretically study harmonically trapped one-dimensional Bose gases (e.g., (7)Li, (23)Na, (39)K, (87)Rb, etc.) with multibands occupied, focusing on effects of higher-energy bands. Combining the Ginzburg-Landau theory with bosonization techniques, we predict that the repulsive interaction between higher-band bosons and the quantum fluctuation can induce the ground state with a finite angular momentum around the trapped axis. In this state, the Z(2) reflection symmetry (clockwise or anticlockwise rotations) is spontaneously broken.

We present a quantum theory for one-dimensional spin-1/2 multiferroics, where<br /> the vector spin chirality couples with the electric polarization. Based on<br /> exact diagonalization and bosonization, it is shown that quantum fluctuations<br /> appreciably reduce the chiral ordering amplitude and the associated<br /> ferroelectric polarization. This yields nearly collinear spin correlations in<br /> short-range scales, in qualitative agreement with recent neutron scattering<br /> experiments. There appear gapless chirality excitations described by phasons<br /> and new solitons, which can be experimentally verified from the low-energy<br /> dielectric response.

We propose a mechanism of a vector chiral long-range order in two-leg spin- 1 2 and spin-1 antiferromagnetic ladders with four-spin exchanges and a Zeeman term. It is known that for one-dimensional quantum systems, spontaneous breakdown of continuous symmetries is generally forbidden. Any vector chiral order hence does not appear in spin-rotationally [SU(2)]-symmetric spin ladders. However, if a magnetic field is added along the Sz axis of ladders and the SU(2) symmetry is reduced to the U(1) one, the z component of a vector chiral order can emerge with the remaining U(1) symmetry unbroken. Making use of Abelian bosonization techniques, we actually show that a certain type of four-spin exchange can yield a vector chiral long-range order in spin- 1 2 and spin-1 ladders under a magnetic field. In the chiral-ordered phase, the Z2 interchain-parity (i.e., chain-exchange) symmetry is spontaneously broken. We also consider effects of perturbations breaking the parity symmetry. © 2007 The American Physical Society.

The frustrated three-leg antiferromagnetic spin-1/2 tube with a weak interchain coupling in a magnetic field is investigated by means of Abelian bosonization techniques. It is clearly shown that a vector chiral long-range order and a one-component Tomonaga-Luttinger liquid coexist in a wide magnetic-field region from a state with a small magnetization to a nearly saturated one. The chiral order is predicted to still survive in the intermediate plateau state. We further predict that (even) when the strength of one bond in the three rung couplings is decreased (increased), an Ising-type quantum phase transition takes place and the chirality vanishes (no singular phenomena occur and the chiral order is maintained). Even without magnetic fields, the chiral order would also be present if the spin tube possesses easy-plane anisotropy.

An S = (1)/(2) three-leg antiferromagnetic spin nanotube is investigated using the DMRG method and the level spectroscopy analysis combined with the numerical exact diagonalization. It is known that the system has a spin gap, when the three rung couplings are equivalent. In this paper, we see that as one of the three rung exchanges varies, a quantum phase transition occurs at a critical value of the varied rung exchange, and then the system is in a gapless Tomonaga-Luttinger-liquid phase. A ground-state phase diagram containing this phase transition is obtained by the phenomenological renormalization. (c) 2006 Published by Elsevier B.V.

Using the exact results of the O (3) nonlinear sigma model (NLSM) and a few quantitative numerical data for integer-spin antiferromagnetic (AF) chains, we systematically estimate all magnon excitation energies of N -leg integer-spin AF ladders and tubes in the weak-interchain-coupling regime. Our method is based on a first-order perturbation theory for the strength of the interchain coupling. It can deal with any kind of interchain interactions, in principle. We confirm that results of the perturbation theory are in good agreement with those of a quantum Monte Carlo simulation and with our recent study based on a saddle-point approximation of the NLSM. Our theory further supports the existence of a Haldane (gapped) phase even in a d -dimensional (d≥2) spatially anisotropic integer-spin AF model, if the exchange coupling in one direction is sufficiently strong compared with those in all the other directions. The strategy in this paper is applicable to other N -leg systems consisting of gapped chains which low-energy physics is exactly or quantitatively known. © 2007 The American Physical Society.

The low-energy physics of three-leg frustrated antiferromagnetic spin-S tubes in the vicinity of the upper critical field are studied. Utilizing the effective field theory based on the spin-wave approximation, we argue that in the intermediate-interchain-coupling regime, the ground state exhibits a vector chiral order or an inhomogeneous magnetization for the interchain (rung) direction and the low-energy excitations are described by a one-component Tomonaga-Luttinger liquid (TLL). In both chiral and inhomogeneous phases, the Z(2) parity symmetry along the rung direction is spontaneously broken. It is also predicted that a two-component TLL appears and all the symmetries are restored in the strong-rung-coupling case.

Using the exact results of the O(3) nonlinear sigma model (NLSM) and a few quantitative numerical data for integer-spin antiferromagnetic (AF) chains, we systematically estimate all magnon excitation energies of N-leg integer-spin AF ladders and tubes in the weak-interchain-coupling regime. Our method is based on a first-order perturbation theory for the strength of the interchain coupling. It can deal with any kind of interchain interactions, in principle. We confirm that results of the perturbation theory are in good agreement with those of a quantum Monte Carlo simulation and with our recent study based on a saddle-point approximation of the NLSM [Phys. Rev. B 72, 104438 (2005)]. Our theory further supports the existence of a Haldane (gapped) phase even in a d-dimensional (d &gt;= 2) spatially anisotropic integer-spin AF model, if the exchange coupling in one direction is sufficiently strong compared with those in all the other directions. The strategy in this paper is applicable to other N-leg systems consisting of gapped chains which low-energy physics is exactly or quantitatively known.

A bosonized-field-theory representation of spin operators in the uniform-field-induced Tomonaga-Luttinger-liquid (TLL) phase in spin-1 Haldane chains is formulated by means of the non-Abelian (Tsvelik's Majorana fermion theory) and the Abelian bosonizations and Furusaki-Zhang technique. It contains massive magnon fields as well as massless boson fields. From it, asymptotic forms of spin correlation functions in the TLL phase are completely determined. Applying the formula, we further discuss the effects of perturbations (bond alternation, single-ion anisotropy terms, staggered fields, etc) for the TLL state, and the string order parameter. Throughout the paper, we often consider in some detail how the symmetry operations of the Haldane chains are translated in the low-energy effective theory.

Recently some quantum spin systems on tube lattices, so-called spin nanotubes, have been synthesized. They are expected to be interesting low-dimensional systems like the carbon nanotubes. As a first step of theoretical study oil the spin nanotube, we investigate the S = 1/2 three-leg spin tube, which is the simplest one, using numerical analyses of finite clusters and a finite-size scaling technique. The spin gap, which is one of the most interesting quantities reflecting the macroscopic quantum effect, was revealed to be open for ally finite rung exchange couplings, in contrast to the three-leg spin ladder system which is gapless. We also found a quantum phase transition caused by an asymmetric rung interaction. When one of the three rung coupling constants is changed, the spin gap vanishes very rapidly. (c) 2005 Elsevier B.V. All rights reserved.

We investigate the low-energy properties, especially the low-energy excitation structures, of N-leg integer-spin ladders and tubes with an antiferromagnetic (AF) intrachain coupling. In the odd-leg tubes, the AF rung coupling causes the frustration. To treat all ladders and tubes systematically, we apply Senechal's method [Phys. Rev. B 52, 15319 (1995)], based on the nonlinear sigma model, together with a saddle-point approximation. This strategy is valid in the weak interchain (rung) coupling regime. We show that all frustrated tubes possess sixfold degenerate spin-1 magnon bands, as the lowest excitations, while other ladders and tubes have a standard triply degenerate bands. We also consider effects of four kinds of Zeeman terms: uniform, staggered only along the rung, only along the chain, or both directions. The above prediction of the no-field case implies that a sufficiently strong uniform field yields a two-component Tomonaga-Luttinger liquid (TLL) due to the condensation of doubly degenerate lowest magnons in frustrated tubes. In contrast, the field induces a standard one-component TLL in all other systems. This is supported by symmetry and bosonization arguments based on the Ginzburg-Landau theory. The bosonization also suggests that the two-component TLL vanishes and a one-component TLL appears, when the uniform field becomes larger for the second lowest magnon bands to touch the zero-energy line. This transition could be observed as a cusp singularity in the magnetization process. When the field is staggered only along the rung direction, it is implied that the lowest doubly-degenerate bands fall down with the field increasing in all systems. For final two cases where the fields are staggered along the chain, it is showed that at least in the weak rung-coupling region, the lowest-excitation gap grows with the field increasing, and no critical phenomena occurs. Furthermore, for the ladders of the final two cases, we predict that the inhomogeneous magnetization along the rung occurs, and the frustration between the field and the rung coupling can induce the magnetization pointing to the opposite direction to the field. All the analyses suggest that the emergence of the doubly degenerate transverse magnons and the single longitudinal one is universal for the one-dimensional AF spin systems with a weak staggered field.

We investigate the elementary excitations of the recently synthesized single-chain magnets, which consist of Mn and Ni ions, and some related systems using the numerical exact diagonalization of finite-size clusters. It is found that, as the easy-axis anisotropy D increases, a crossover of the lowest-lying elementary excitation should exist between the spin wave and Ising-like excitations. In the realistic materials both excitations are revealed to be comparably significant.

This study addresses low-energy properties of two-leg spin-1 ladders with antiferromagnetic (AF) intrachain coupling under a uniform or staggered external field H, and a few of their modifications. The generalization to spin-S ladders is also discussed. In the strong AF rung(interchain)-coupling J(perpendicular to) region, degenerate perturbation theory applied to spin-S ladders predicts 2S critical curves in the parameter space (J(perpendicular to),H) for the staggered-field case, in contrast to 2S finite critical regions for the uniform-field case. All critical areas belong to a universality with central charge c=1. On the other hand, we employ Abelian and non-Abelian bosonization techniques in the weak rung-coupling region. They show that in the spin-1 ladder, a sufficiently strong uniform field engenders a c=1 critical state regardless of the sign of J(perpendicular to), whereas the staggered field is expected not to yield any singular phenomena. From the bosonization techniques, new field-theoretical expressions of string order parameters in the spin-1 systems are also proposed.

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 higher (two or three) dimensional spin system analytically. In particular, in the case where the staggered field and the interchain 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 noncompetitive case. When the interchain 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. © 2004 The American Physical Society.

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 higher (two or three) dimensional spin system analytically. In particular, in the case where the staggered field and the interchain 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 noncompetitive case. When the interchain 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.

We study weakly coupled S = 1/2 quantum Heisenberg antiferromagnetic chains in an effective staggered field. Applying mean-field (MF) theory, spin-wave theory and chain MF (CMF) theory, we can see analytically some effects of the staggered field in this higher dimensional spin system. In particular, when the staggered field and the inter-chain interaction compete with each other, we conjecture from the MF theory that a nontrivial phase is present. The spin wave theory predicts that the behavior of the gaps induced by a staggered field is different between the competitive case and the non-competitive case. When the inter-chain interactions are weak enough, we can improve the MF phase diagram by using CMF theory and the analytical results of field theories. The ordered phase region predicted by the CMF theory is fairly smaller than one of the MF theory. Cu-benzoate, CuCl2 (.) 2DMSO (dimethylsulphoxide), BaCu2(Si1-xGex)(2)O-7, etc., could be described by our model in enough low temperature.