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arXiv:cond-mat/0105416 Ā· Journal of Physics A Mathematical and General

Finite-temperature correlations for theUq(š”°š”©(2|1))-invariant generalized Hubbard model

Kazumitsu Sakai, Andreas KlĆ¼mper

Published Sep 21, 2001ā€¢ 7 citations
arXivHTMLPDF

Abstract

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 ( (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 nonlinear 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.

DOI
10.1088/0305-4470/34/39/307

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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 ( (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 nonlinear 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.
We investigate the thermodynamics of a one-dimensional Hubbard model with bond-charge interaction X using the transfer-matrix renormalization-group method. Numerical results for various quantities such as spin and charge susceptibilities, particle densities, specific heat, and thermal correlation lengths are presented and discussed. We compare our data also to results for the exactly solvable case X/t=1X/t=1X/t=1 as well as to bosonization results for weak coupling $X/t\ensuremath{\ll}1,$ which shows excellent agreement. We confirm the existence of a Tomonaga-Luttinger and a Luther-Emery liquid phase, in agreement with previous studies at zero temperature. Thermal singlet-pair-correlation lengths are shown to dominate density and spin correlations for finite temperatures in certain parameter regimes.
Abstract We present a general formula for constructing R-matrices with non-additive spectral parameters associated with a type-I quantum superalgebra. The spectral parameters originate from two one-parameter families of inequivalent finite-dimensional irreducible representations of the quantum superalgebra upon which the R-matrix acts. Applying to the quantum superalgebra Uq(gl(2|1)), we obtain the explicit expression for the Uq(gl(2|1))āˆ’ invariant R-matrix which is of non-difference form in spectral parameters. Using this RĀ­ matrix we derive a new two-parameter integrable model of strongly correlated electrons with pure imaginary pair hopping terms.
A Trotter-Suzuki mapping is used to calculate the finite-temperature properties of the one-dimensional supersymmetric t āˆ’ J model. This approach allows for the exact calculation of various thermodynamical properties by means of the quantum transfer matrix (QTM). The free energy and other interesting quantities are obtained such as the specific heat and compressibility. For the largest eigenvalue of the QTM leading to the free energy a set of just two non-linear integral equations is presented. These equations are studied analytically and numerically for different particle densities and temperatures. The structure of the specific heat is discussed in terms of the elementary charge as well as spin excitations. Special emphasis is placed on the study of the low-temperature behavior confirming scaling predictions by conformal field theory and Luttinger liquid theory. To our knowledge this is the first complete investigation of a strongly correlated electron system on a lattice at finite temperature.
The supersymmetric tJ model in one dimension is investigated by means of the quantum transfer matrix (QTM). The free energy of the quantum system is given by just the largest eigenvalue of the QTM whereas the next-largest ones determine the correlation lengths at finite temperature. The first step of the analysis consists of an embedding of the QTM into a family of commuting matrices. In the second step the eigenvalues equations are derived by an algebraic Bethe ansatz. Finally, the eigenvalue equations are transformed into a set of nonlinear integral equations. Some numerical results are presented. The specific heat for instance shows the typical Luttinger liquid behavior at low temperatures.