arXiv subjects

Kazumitsu Sakai

Publications and source records attributed to Kazumitsu Sakai.

43 records · Page 3Linked to original sources

arXiv2001

The thermal conductivity of the spin-1/2 XXZ chain at arbitrary temperature

Motivated by recent investigations of transport properties of strongly correlated 1d models and thermal conductivity measurements of quasi 1d magnetic systems we present results for the integrable spin-1/2 $XXZ$ chain. The thermal conductivity $κ(ω)$ of this model has $\Reκ(ω)=\tildeκδ(ω)$, i.e. it is infinite for zero frequency $ω$. The weight $\tildeκ$ of the delta peak is calculated exactly by a lattice path integral formulation. Numerical results for wide ranges of temperature and anisotropy are presented. The low and high temperature limits are studied analytically.

cond-mat.stat-mech↗

arXiv2001

Finite temperature correlations for the U_q(sl(2|1))-invariant generalized Hubbard model

We study an integrable model of one-dimensional strongly correlated electrons at finite temperature by explicit calculation of the correlation lengths of various correlation functions. The model is invariant with respect to the quantum superalgebra U_q(sl(2|1)) and characterized by the Hubbard interaction, correlated hopping and pair-hopping terms. Using the integrability, the graded quantum transfer matrix is constructed. From the analyticity of its eigenvalues, a closed set of non-linear integral equations is derived which describe the thermodynamical quantities and the finite temperature correlations. The results show a crossover from a regime with dominating density-density correlations to a regime with dominating superconducting pair correlations. Analytical calculations in the low temperature limit are also discussed.

cond-mat.stat-mech↗

arXiv2000

Thermodynamics of osp(1|2) Integrable Spin Chain: Finite Size Correction

This note is a supplement to our previous papers: Mod. Phys. Lett. A14 (1999) 2427 (math-ph/9911010); Int. J. Mod. Phys. A15 (2000) 2329 (math-ph/9912014). The thermodynamic Bethe ansatz (TBA) equation for an integrable spin chain related to the Lie superalgebra osp(1|2) is analyzed. The central charge determined by low temperature asymptotics of the specific heat can be expressed by the Rogers dilogarithmic function, and identified to be 1. Solving the TBA equation numerically, we evaluate the several thermodynamic quantities. The excited state TBA equation is also discussed.

cond-mat.stat-mech↗

arXiv2000

Thermodynamic Bethe ansatz equation from fusion hierarchy of osp(1|2) integrable spin chain

The thermodynamic Bethe ansatz (TBA) and the excited state TBA equations for an integrable spin chain related to the Lie superalgebra osp(1|2) are proposed by the quantum transfer matrix (QTM) method. We introduce the fusion hierarchy of the QTM and derive the functional relations among them (T-system) and their certain combinations (Y-system). Their analytical property leads to the non-linear integral equations which describe the free energy and the correlation length at any finite temperatures. With regard to the free energy, they coincide with the TBA equation (math-ph/9911010, Mod. Phys. Lett. A, 14, 2427 (1999)) based on the string hypothesis.

math-ph↗

arXiv1999

Excited state TBA and functional relations in spinless Fermion model

The excited state thermodynamic Bethe ansatz (TBA) equations for the spinless Fermion model are presented by the quantum transfer matrix (QTM) approach. We introduce a more general family called T-functions and explore functional relations among them (T-system) and their certain combinations (Y-system). {}From their analytical property, we derive a closed set of non-linear integral equations which characterize the correlation length of $ $ at any finite temperatures. Solving these equations numerically, we explicitly determine the correlation length, which coincides with earlier results with high accuracy.

cond-mat.stat-mech↗

arXiv1999

Commuting quantum transfer matrix approach to intrinsic Fermion system: Correlation length of a spinless Fermion model

The quantum transfer matrix (QTM) approach to integrable lattice Fermion systems is presented. As a simple case we treat the spinless Fermion model with repulsive interaction in critical regime. We derive a set of non-linear integral equations which characterize the free energy and the correlation length of $ $ for arbitrary particle density at any finite temperatures. The correlation length is determined by solving the integral equations numerically. Especially in low temperature limit this result agrees with the prediction from conformal field theory (CFT) with high accuracy.

cond-mat.stat-mech↗

arXiv1998

Continued fraction TBA and functional relations in XXZ model at root of unity

Thermodynamics of the spin 1/2 XXZ model is studied in the critical regime using the quantum transfer matrix (QTM) approach. We find functional relations indexed by the Takahashi-Suzuki numbers among the fusion hierarchy of the QTM's (T-system) and their certain combinations (Y-system). By investigating analyticity of the latter, we derive a closed set of non-linear integral equations which characterize the free energy and the correlation lengths for both and at any finite temperatures. Concerning the free energy, they exactly coincide with Takahashi-Suzuki's TBA equations based on the string hypothesis. By solving the integral equations numerically the correlation lengths are determined, which agrees with the earlier results in the low temperature limit.

math.QA↗