arXiv subjects

T. Fukui

Publications and source records attributed to T. Fukui.

86 records · Page 5Linked to original sources

arXiv1997

Mixed-Spin Ladders and Plaquette Spin Chains

We investigate low-energy properties of a generalized spin ladder model with both of the spin alternation and the bond alternation, which allows us to systematically study not only ladder systems but also alternating spin chains. By exploiting non-linear $σ$ model techniques we study the model with particular emphasis on the competition between gapful and gapless states. Our approach turns out to provide a more consistent semi-classical description of alternating spin chains than that in the previous work. We also study a closely related model, i.e., a spin chain with plaquette structure, and show that frustration causes little effect on its low-energy properties so far as the strength of frustration is weaker than a certain critical value.

cond-mat.str-el↗

arXiv1997

Alternating-Spin Ladders

We investigate a two-leg spin ladder system composed of alternating-spin chains with two-different kind of spins. The fixed point properties are discussed by using spin-wave analysis and non-linear sigma model techniques. The model contains various massive phases, reflecting the interplay between the bond-alternation and the spin-alternation.

cond-mat.stat-mech↗

arXiv1997

Low-Energy Properties of Regularly Depleted Spin Ladders

We investigate a model for the regularly depleted two-leg spin ladder systems. By using Lieb-Schultz-Mattis theorem, it is rigorously shown that this model realizes massless excitations or, alternatively, a degenerate ground state, although the original spin ladder system has a spin gap and a unique ground state. The ground state of the depleted model is either a spin singlet or partially ferromagnetic reflecting topological properties of the depleted sites. In order to show that the low-energy excitations are indeed massless, we proceed our analysis in two different ways by resorting to effective field theories. We first investigate an effective weak-coupling model in terms of renormalization group methods. Although the tendency to massless spin excitations is seen in the strong coupling regime, it turns out that the model is still massive for any finite coupling, implying that a conventional weak-coupling approach is not efficient to describe massless modes in our model. To overcome this difficulty, we further study low-energy properties of the depleted spin model by mapping on the non-linear sigma model, and confirm that the massless spin excitation indeed occur.

cond-mat.stat-mech↗

arXiv1997

Alternating spin chains with singlet ground states

We investigate low-energy properties of the alternating spin chain model composed of spin $s_1$ and $s_2$ with a singlet ground state. After examining the spin-wave spectrum in detail, we map low-energy spin excitations to the O(3) non-linear sigma model in order to take into account quantum fluctuations. Analyzing the topological term in the resulting sigma model, we discuss how the massless or massive excitations are developed, especially according to the topological nature of the alternating spin system.

cond-mat.stat-mech↗

arXiv1997

Spin Chains with Periodic Array of Impurities

We investigate the spin chain model composed of periodic array of two kinds of spins $S_1$ and $S_2$, which allows us to study the spin chains with impurities as well as the alternating spin chains in a unified fashion. By using the Lieb-Shultz-Mattis theorem, we first study the model rigorously, and then by mapping it to the non-linear sigma model, we extensively investigate low-energy properties with particular emphasis on the competition between the massive and massless phases.

cond-mat.stat-mech↗

arXiv1996

SU(ν) Generalization of Twisted Haldane-Shastry Model

The SU($ν$) generalized Haldane-Shastry spin chain with $1/r^2$ interaction is studied with twisted boundary conditions. The exact wavefunctions of Jastrow type are obtained for every rational value of the twist angle in unit of $2π$. The spectral flow of the ground state is then discussed as a function of the twist angle. By resorting to the motif picture in the Bethe ansatz method, we show that the period of the spectral flow is $ν$, which is determined by the statistical interaction in exclusion statistics.

cond-mat.stat-mech↗

arXiv1996

Spectral flow in the supersymmetric $t$-$J$ model with a $1/r^2$ interaction

The spectral flow in the supersymmetric {\it t-J} model with $1/r^2$ interaction is studied by analyzing the exact spectrum with twisted boundary conditions. The spectral flows for the charge and spin sectors are shown to nicely fit in with the motif picture in the asymptotic Bethe ansatz. Although fractional exclusion statistics for the spin sector clearly shows up in the period of the spectral flow at half filling, such a property is generally hidden once any number of holes are doped, because the commensurability condition in the motif is not met in the metallic phase.

cond-mat↗

arXiv1996

Adiabatic Ground-State Properties of Spin Chains with Twisted Boundary Conditions

We study the Heisenberg spin chain with twisted boundary conditions, focusing on the adiabatic flow of the energy spectrum as a function of the twist angle. In terms of effective field theory for the nearest-neighbor model, we show that the period 2 (in unit $2π$) obtained by Sutherland and Shastry arises from irrelevant perturbations around the massless fixed point, and that this period may be rather general for one-dimensional interacting lattice models at half filling. In contrast, the period for the Haldane-Shastry spin model with $1/r^2$ interaction has a different and unique origin for the period, namely, it reflects fractional statistics in Haldane's sense.

cond-mat↗

arXiv1996

Exact solution and spectral flow for twisted Haldane-Shastry model

The exact solution of the spin chain model with $1/r^2$ exchange is found for twisted boundary conditions. The spectrum thus obtained can be reproduced by the asymptotic Bethe ansatz. The spectral flow of each eigenstate is determined exactly as a function of the twist angle. We find that the period $4π$ for the ground state nicely fits in with the notion of fractional exclusion statistics.

cond-mat↗

arXiv1995

Spin-$S$ generalization of fractional exclusion statistics

We study fractional exclusion statistics for quantum systems with SU(2) symmetry (arbitrary spin $S$), by generalizing the thermodynamic equations with squeezed strings proposed by Ha and Haldane. The bare hole distributions as well as the statistical interaction defined by an infinite-dimensional matrix specify the universality class. It is shown that the system is described by the level-$2S$ WZW model and has a close relationship to non-abelian fractional quantum Hall states. As a low-energy effective theory, the sector of {\it massless} Z$_{2S}$ parafermions is extracted, whose statistical interaction is given by a finite-dimensional matrix.

cond-mat↗

arXiv1995

Transport coefficients, effective charge and mass for multicomponent systems with fractional exclusion statistics

Transport properties of the multicomponent quantum many-body systems obeying Haldane's fractional exclusion statistics are studied in one dimension. By computing the finite-size spectrum under twisted boundary conditions, we explicitly express the conductivity and the conductance in terms of statistical interactions. Through this analysis, the effective charge and effective mass for collective excitations are determined. We apply the results for $1/r^2$ quantum systems as well as for correlated electron systems.

cond-mat↗

arXiv1993

A coherent state associated with shape-invariant potentials

An algebraic treatment of shape-invariant potentials is discussed. By introducing an operator which reparametrizes wavefunctions, the shape-invariance condition can be related to a generalized Heisenberg- Weyl algebra. It is shown that this makes it possible to define a coherent state associated with the shape-invariant potentials.

hep-th↗

arXiv1993

Shape-invariant potentials and an associated coherent state

An algebraic treatment of shape-invariant potentials in supersymmetric quantum mechanics is discussed. By introducing an operator which reparametrizes wave functions, the shape-invariance condition can be related to a oscillator-like algebra. It makes possible to define a coherent state associated with the shape-invariant potentials. For a large class of such potentials, it is shown that the introduced coherent state has the property of resolution of unity.

hep-th↗

arXiv1993

Self-Similar Potentials and q-Coherent States

The self-similar potentials are formulated in terms of the shape-invariance. Based on it, a coherent state associated with the shape-invariant potentials is calculated in case of the self-similar potentials. It is shown that it reduces to the q-deformed coherent state.

hep-th↗