Exact thermodynamics and Luttinger liquid properties of the integrable t-J model

Abstract

A Trotter-Suzuki mapping is used to calculate the finite-temperature properties of the one-dimensional supersymmetric t − 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. *

Spinons in magnetic chains of arbitrary spins at finite temperatures

“…This has been already demonstrated for several models in highly correlated 1D electron systems including the supersymmetric t − J model [14], the supersymmetric extended Hubbard model [15] and the Hubbard model [17]. There the exact thermodynamics are formulated in terms of "spinons" and "holons", although they lose sense at sufficiently high temperatures.…”

Integrability of quantum chains: Theory and applications to the spin-1/2 XXZ chain

“…particles. Important examples of these systems are the Heisenberg model [1,2], tJ- [3][4][5] and Hubbard models [6,7] The computational basis for the work on integrable quantum chains is the Bethe ansatz yielding a set of coupled non-linear equations for 1-particle wave-numbers (Bethe ansatz roots). Many studies of the Bethe ansatz equations were directed at the ground-states of the considered systems and have revealed interesting non-Fermi liquid properties such as algebraically decaying correlation functions with non-integer exponents and low-lying excitations of different types, i.e.…”

THERMODYNAMIC BETHE ANSATZ EQUATION FROM FUSION HIERARCHY OF osp(1|2) INTEGRABLE SPIN CHAIN

“…Since the QTM has a finite gap, the original problem for the calculation of the partition function reduces to finding the single largest eigenvalue of the QTM. To evaluate it actually, we utilize the underlying integrable structure, which admits introduction of the "commuting" QTM with a complex parameter v [52,53,54,55,56,57]. Furthermore, we introduce some auxiliary functions including the QTM itself, which satisfy functional relations.…”