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arXiv:cond-mat/9604191 · Physical review. B, Condensed matter

Variational study of the spin-gap phase of the one-dimensionalt-Jmodel

Y. C. Chen, T. K. Lee

Published Oct 1, 1996• 9 citations
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Abstract

We propose a correlated spin-singlet-pair wave function to describe the spin-gap phase of the one-dimensional t-J model at low density and large J/t. In addition to having singlet pairs, this wave function has a Jastrow factor with a variational parameter \ensuremath{\nu}. Several correlation functions are calculated by using the variational Monte Carlo method. The result shows the expected long-range behavior of the Luther-Emery phase with the Luttinger exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ related to \ensuremath{\nu}, ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$=1/2\ensuremath{\nu}. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.9062

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Physical review. B, Condensed matter•Aug 1, 1991•57 citations
We propose a correlated spin-singlet-pair wave function to describe the spin-gap phase of the one-dimensional t-J model at low density and large J/t. In addition to having singlet pairs, this wave function has a Jastrow factor with a variational parameter \ensuremath{\nu}. Several correlation functions are calculated by using the variational Monte Carlo method. The result shows the expected long-range behavior of the Luther-Emery phase with the Luttinger exponent K\ensuremathρ{\mathit{K}}_{\mathrm{\ensuremath{\rho}}}K\ensuremathρ​ related to \ensuremath{\nu}, K\ensuremathρ{\mathit{K}}_{\mathrm{\ensuremath{\rho}}}K\ensuremathρ​=1/2\ensuremath{\nu}. \textcopyright{} 1996 The American Physical Society.
The one-dimensional t-J model is investigated by the variational Monte Carlo method. A variational wave function based on the Bethe-ansatz solution is proposed, where the spin-charge separation is realized and a long-range correlation factor of Jastrow-type is included. In most regions of the phase diagram, this wave function provides an excellent description of the ground-state properties characterized as a Tomonaga-Luttinger liquid; both the amplitude and exponent of correlation functions are correctly reproduced. For the spin-gap phase, another trial state of correlated singlet pairs with a Jastrow factor is introduced. This wave function shows generalized Luther-Emery-liquid behavior, exhibiting enhanced superconducting correlations and exponential decay of the spin correlation function. Using these two variational wave functions, the whole phase diagram is determined. In addition, relations between the correlation exponent and variational parameters in the trial functions are derived. \textcopyright{} 1996 The American Physical Society.
The one-dimensional (1D) t-J model is investigated by using a Gutzwiller-Jastrow-type variation method and the exact diagonalization of small systems. Variational expectation values are estimated by the variational Monte Carlo method with sufficient accuracy. First, we give detailed descriptions of the preceding paper [Phys. Rev. Lett. 67, 3610 (1991)], where we discussed the properties of the Fermi-liquid-type Jastrow wave function as well as the Gutzwiller wave function. Secondly, these wave functions are compared with the Tomonaga-Luttinger-liquid-type wave function proposed by Hellberg and Mele. It is found that the correlation factors in short distances control bulk quantities like energy and the magnitude of the correlation functions, while the long-range part of the correlation factors determines the critical behavior of correlation functions. Finally, using these functions, charge, spin susceptibilities, and magnetization curve are estimated, which agree with the exact results. It is shown that the Mott transition in the 1D t-J model is quite different from the Brinkman-Rice transition. \textcopyright{} 1996 The American Physical Society.
We study the t-J model in one dimension by numerically projecting the true ground state from a Luttinger-liquid trial wave function. We find the model exhibits Luttinger-liquid behavior for most of the phase diagram in which interaction strength and density are varied. However, at small densities and high interaction strengths a new phase with a gap to spin excitations and enhanced superconducting correlations is found. We show that this phase is a Luther-Emery liquid and study its correlation functions.
The momentum distribution and the spin-correlation functions are studied for the one-dimensional t-J model, in which the exchange interaction J is anisotropic. The discussion is focused on the nontrivial limit that J is much smaller than t. In this limit the exact ground-state wave function is a product of the spinless-fermion Slater determinant and the spin-wave function of the s=1/2 anisotropic Heisenberg antiferromagnet. With this wave function, correlation functions are calculated explicitly for finite but large systems and the nature of their singularities is studied. It is found that for the XY-like anisotropy the critical behavior of correlation functions can be described by the Tomonaga-Luttinger model, while for the Ising-like anisotropy the model seems to belong to the universality class of the Luther-Emery model of the one-dimensional electron gas.
The physics of the one-dimensional t-J model may be determined at J/t\ensuremath{\rightarrow}0 (i.e., the U/t\ensuremath{\rightarrow}\ensuremath{\infty} limit of the repulsive Hubbard model) and at J/t=2 with the use of the Bethe ansatz. To get a full understanding of the charge and spin correlation functions for all values of J/t, one has to resort to numerical methods. We have used two numerical methods (the world-line quantum Monte Carlo algorithm and the quantum transfer-matrix algorithm) to get information on charge and spin static structure factors, pairing correlations, and critical exponents. The (1+1)-dimensional classical system corresponding to the one-dimensional t-J model, on which the Monte Carlo technique is used, is identified to a fifteen-vertex model. We show that the t-J model undergoes phase separation at large values of J/t. Before phase separation, both critical exponents and pairing correlations in the extended s-wave channel favor the onset of superconductivity. For low values of J/t, the model shows a U/t\ensuremath{\rightarrow}\ensuremath{\infty} Hubbard-like character.