Exact calculation of thermodynamical quantities of the integrable t-J model

The specific heat and the compressibility for the integrable t-J model are calculated showing Luttinger liquid behavior for low temperatures. A Trotter-Suzuki mapping and the quantum transfer matrix approach are utilized. Using an algebraic Bethe ansatz this method permits the exact calculation of the free energy and related quantities. A set of just two non-linear integral equations determining these quantities is studied for various particle densities and temperatures. The structure of the specific heat is discussed in terms of the elementary charge as well as spin excitations.Comment: 4 pages, 5 Postscript figures, uses epsf.sty and revtex, tar'ed, gzip'ed and uuencode

Exact trimer ground states on a spin-1 chain

We construct a new spin-1 model on a chain. Its ground state is determined exactly which is three-fold degenerate by breaking translational invariance. Thus we have trimerization. Excited states cannot be obtained exactly, but we determine a few low-lying ones by using trial states, among them solitons

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.Comment: 40 pages, 19 figure

Nonlinear integral equations for the thermodynamics of the sl(4)-symmetric Uimin-Sutherland model

We derive a finite set of nonlinear integral equations (NLIE) for the thermodynamics of the one-dimensional sl(4)-symmetric Uimin-Sutherland model. Our NLIE can be evaluated numerically for arbitrary finite temperature and chemical potentials. We recover the NLIE for sl(3) as a limiting case. In comparison to other recently derived NLIE, the evaluation at low temperature poses no problem in our formulation. The model shows a rich ground-state phase diagram. We obtain the critical fields from the T to zero limit of our NLIE. As an example for the application of the NLIE, we give numerical results for the SU(4) spin-orbital model. The magnetic susceptibility shows divergences at critical fields in the low-temperature limit and logarithmic singularities for zero magnetic field.Comment: 32 pages, 7 figures; references added, minor corrections, final versio

Integral representations for correlation functions of the XXZ chain at finite temperature

We derive a novel multiple integral representation for a generating function of the \s^z-\s^z correlation functions of the spin-\2 XXZ chain at finite temperature and finite, longitudinal magnetic field. Our work combines algebraic Bethe ansatz techniques for the calculation of matrix elements with the quantum transfer matrix approach to thermodynamics.Comment: 33 pages, 2 figures, v2: 2 typos corrected, 1 figure adde

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.Comment: 4 page

Lattice path integral approach to the one-dimensional Kondo model

An integrable Anderson-like impurity model in a correlated host is derived from a gl(2$|$1)-symmetric transfer matrix by means of the Quantum-Inverse-Scattering-Method (QISM). Using the Quantum Transfer Matrix technique, free energy contributions of both the bulk and the impurity are calculated exactly. As a special case, the limit of a localized moment in a free bulk (Kondo limit) is performed in the Hamiltonian and in the free energy. In this case, high- and low-temperature scales are calculated with high accuracy.Comment: 26 pages, 9 figure

The Hubbard chain at finite temperatures: ab initio calculations of Tomonaga-Luttinger liquid properties

We present a novel treatment of finite temperature properties of the one-dimensional Hubbard model. Our approach is based on a Trotter-Suzuki mapping utilizing Shastry's classical model and a subsequent investigation of the quantum transfer matrix. We derive non-linear integral equations for three auxiliary functions which have a clear physical interpretation of elementary excitations of spin type and charge excitations in lower and upper Hubbard bands. This allows for a transparent analytical study of certain limiting cases as well as for precise numerical investigations. We present data for the specific heat, magnetic and charge susceptibilities for various particle densities and coupling strengths U. The structure exposed by these curves is discussed in terms of the elementary charge and spin excitations. Special emphasis is placed on the study of the low-temperature behavior within our ab initio approach confirming the scaling predictions by Tomonaga-Luttinger liquid theory. In addition we make contact with the ``dressed energy'' formalism established for the analysis of ground state properties.Comment: 33 pages including 24 Postscript figure