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Physical review. B, Condensed matter

New phase in the one-dimensionalt-Jmodel

Y.-C. Chen, Ting-Kuo Lee

Published May 1, 1993• 24 citations
Publisher

Abstract

A new phase of a gas of pairs of electrons bounded in a singlet state is found in the one-dimensional t-J model for J>2t and the density of electrons less than 0.2. This phase was conjectured in the study of the diagonalization of small lattices [Phys. Rev. Lett. 66, 2388 (1991)]. The existence of this new phase for much larger lattice sizes is demonstrated by a combination of two numerical methods, the variational Monte Carlo and the power method. A trial wave function for this phase is proposed and shown to be in good agreement with the ground state obtained by the power method.

DOI
10.1103/physrevb.47.11548

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Physical review. B, Condensed matter•Nov 1, 1992•47 citations
A new phase of a gas of pairs of electrons bounded in a singlet state is found in the one-dimensional t-J model for J>2t and the density of electrons less than 0.2. This phase was conjectured in the study of the diagonalization of small lattices [Phys. Rev. Lett. 66, 2388 (1991)]. The existence of this new phase for much larger lattice sizes is demonstrated by a combination of two numerical methods, the variational Monte Carlo and the power method. A trial wave function for this phase is proposed and shown to be in good agreement with the ground state obtained by the power method.
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.
Ground-state properties of the one-dimensional t-J model are studied by using exact diagonalization of small systems and compared with those found with Gutzwiller-Jastrow--type variational functions. Near the supersymmetric case (J/t=2), the Gutzwiller wave function is an extremely good trial function for all electron densities. It reproduces momentum distribution and correlation functions of the exact ground state except for critical behaviors. For J/t2 (>2), the ground-state properties are well described by Jastrow functions with repulsive (attractive) intersite correlations.
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 develop a general numerical method to study the zero-temperature properties of strongly correlated electron models on large lattices. The technique, which resembles Green's-function Monte Carlo, projects the ground-state component from a trial wave function with no approximations. We use this method to determine the phase diagram of the two-dimensional $t\ensuremath{-}J$ model, using the Maxwell construction to investigate electronic phase separation. The shell effects of fermions on finite-sized periodic lattices are minimized by keeping the number of electrons fixed at a closed-shell configuration and varying the size of the lattice. Results obtained for various electron numbers corresponding to different closed shells indicate that the finite-size effects in our calculation are small. For any value of interaction strength, we find that there is always a value of the electron density above which the system can lower its energy by forming a two-component phase separated state. Our results are compared with other calculations on the $t\ensuremath{-}J$ model. We find that the most accurate results are consistent with phase separation at all interaction strengths.
We study the t-J model in one and two dimensions. It is shown that superconducting correlations at large distances are enhanced at doping 〈n〉=1/2, and near the region of phase separation. Including a nearest-neighbor density-density repulsion term of strength V, and working at large V/t and J/t, our results can be explained using a previously discussed variational state where electrons are paired in singlets without cluster formation, in analogy to the attractive Hubbard model. We argue that the physics of the t-J-V model is basically independent of the dimension and that a smooth connection exists between small and large V/t. Then, we conjecture that the two-dimensional t-J model should also present strong superconducting correlations near the region of phase separation, at 〈n〉\ensuremath{\sim}1/2. Numerical results both in one and two dimensions support our claims.