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arXiv:1604.08861 · Journal of Statistical Mechanics Theory and Experiment

Exact thermodynamics and phase diagram of integrable t-J model with chiral interaction

T S Tavares, G A P Ribeiro

Published Sep 1, 2016• 0 citations
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Abstract

Abstract We study the phase diagram and finite temperature properties of an integrable generalization of the one-dimensional super-symmetric t-J model containing interactions explicitly breaking parity-time reversal (PT) symmetries. To this purpose, we apply the quantum transfer matrix method which results in a finite set of non-linear integral equations. We obtain numerical solutions to these equations leading to results for thermodynamic quantities as a function of temperature, magnetic field, particle density and staggering parameter. Studying the maxima lines of entropy at low but non zero temperature reveals the phase diagram of the model. There are ten different phases which we may classify in terms of the qualitative behaviour of auxiliary functions, closely related to the dressed energy functions.

DOI
10.1088/1742-5468/2016/09/093103

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Abstract We study the phase diagram and finite temperature properties of an integrable generalization of the one-dimensional super-symmetric t-J model containing interactions explicitly breaking parity-time reversal (PT) symmetries. To this purpose, we apply the quantum transfer matrix method which results in a finite set of non-linear integral equations. We obtain numerical solutions to these equations leading to results for thermodynamic quantities as a function of temperature, magnetic field, particle density and staggering parameter. Studying the maxima lines of entropy at low but non zero temperature reveals the phase diagram of the model. There are ten different phases which we may classify in terms of the qualitative behaviour of auxiliary functions, closely related to the dressed energy functions.
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.
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.
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.
[[abstract]]The phase diagram and thermodynamic properties of the Hubbard model in one dimension are calculated numerically within the generalized self-consistent approach over a wide range of temperature T, magnetic field h, interaction strength U/t and electron concentration n. The temperature variation of the transverse magnetization, double occupied sites and chemical potential at various n, U/t and h is also analyzed. The wave vector q for the magnetic order parameter in the vicinity of the half-filling in the metallic phase shows a crossover from incommensurate magnetic phase (0 < q < pi) into the state with strong antiferromagnetic correlations (q = pi) as temperature is increased. Overall our numerical results in the approximate theory at finite temperatures are in good quantitative and qualitative agreement with the Bethe-ansatz results.
We consider integrable quantum spin chains with competing interactions. We apply the quantum transfer matrix approach to these spin chains. This allows us to derive a set of nonlinear integral equations for the thermodynamics of these spin chains. We provide numerical solutions of these integral equations for the entropy as a function of magnetic field, temperature and the coupling constant. In addition we describe, at low but finite temperature, the possible scenarios for the ground state diagram for high-spin chain and longer range interchain interactions.
Abstract We analyze the thermodynamics and the critical behavior of the supersymmetric t - J model with long-range interactions. Using the transfer matrix formalism, we obtain a closed-form expression for the free energy per site both for a finite number of sites and in the thermodynamic limit. Our approach, which is different from the usual ones based on the asymptotic Bethe ansatz and generalized exclusion statistics, can in fact be applied to a large class of models whose spectrum is described in terms of supersymmetric Young tableaux and their associated Haldane motifs. In the simplest and most interesting case, we identify the five ground state phases of the model and derive the complete low-temperature asymptotic series of the free energy per site, the magnetization and charge densities, and their susceptibilities. We verify the model’s characteristic spin-charge separation at low temperatures, and show that it holds to all orders in the asymptotic expansion. Using the low-temperature asymptotic expansions of the free energy, we also analyze the critical behavior of the model in each of its ground state phases. While the standard phase is described by two independent conformal field theories (CFTs) with central charge c = 1 in correspondence with the spin and charge sectors, we find that the low-energy behavior of the and phases is that of a single c = 1 CFT. We show that the model exhibits an even richer behavior on the boundary between zero-temperature phases, where it can be non-critical but gapless, critical in the spin sector but not in the charge one, or critical with central charge c = 3/2.