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arXiv:cond-mat/9212031 · Physical review. B, Condensed matter

Spin gap and superconductivity in the one-dimensionalt-Jmodel with Coulomb repulsion

Matthias Troyer, Hirokazu Tsunetsugu, Thomas Maurice Rice, José A. Riera, Elbio R. Dagotto

Published Aug 1, 1993• 32 citations
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Abstract

The one-dimensional t-J model with density-density repulsive interactions is investigated with the use of exact-diagonalization and quantum Monte Carlo methods. A short-range repulsion pushes phase separation to larger values of J/t, and leads to a widened precursor region in which a spin gap and strengthened superconducting correlations appear. The correlation exponent is calculated. On the contrary, a long-range repulsion of form 1/r suppresses superconductivity in the precursor region.

DOI
10.1103/physrevb.48.4002

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Physical review. B, Condensed matter•Nov 1, 1992•47 citations
The one-dimensional t-J model with density-density repulsive interactions is investigated with the use of exact-diagonalization and quantum Monte Carlo methods. A short-range repulsion pushes phase separation to larger values of J/t, and leads to a widened precursor region in which a spin gap and strengthened superconducting correlations appear. The correlation exponent is calculated. On the contrary, a long-range repulsion of form 1/r suppresses superconductivity in the precursor region.
The phase diagram of the one-dimensional t-J model is investigated by analyzing the results of exact diagonalization and the exact solutions at J/t=0 and 2. Phase separation takes place above a critical value of J around Jc{\mathit{J}}_{\mathit{c}}Jc​/t=2.5--3.5 depending on the electron density. In the small-J region, Tomonaga-Luttinger liquid theory holds and its correlation exponents are calculated as a function of J/t and the electron density. Superconducting correlations become dominant in a region between the solvable case (J/t=2) and phase separation. A spin-gap region is also found at low density.
The phase diagram of one-dimensional dimerized t-J model is investigated by exact-diagonalization, quantum tranfer-matrix, and quantum Monte Carlo methods. The spin gap persists near but away from half-filling as well as in a strongly dimerized region, while the charge can be described as a Tomonaga-Luttinger liquid in the entire region. The spin-gap region extends to the weak-dimerization region as well as to the Haldane-gap region. Critical exponents of various correlation functions are discussed. The pairing correlation shows remarkable enhancement and by far dominates over other correlations near half-filling. At quarter filling, charge-gap formation is observed.
We have used exact diagonalization and quantum Monte Carlo methods to study the one-dimensional t-J model including the three-site hopping term derived from the strong-coupling limit of the Hubbard model. The three-site term may be important to superconducting correlations since it allows direct hopping of local singlet electron pairs. The phase diagram is determined for several values of the strength of the three-site term and compared with that of the t-J and Hubbard models. Phase separation, which exists in the t-J model, is suppressed. In the low electron density region the formation of local singlet electron pairs is enhanced, leading to stronger superconducting correlations even for values J/t2. A large spin gap region extends from low electron densities up to high densities. In the low hole density region the superconducting correlations are suppressed at J/t>2.8 in spite of enhanced pair formation. This is because the three-site term, while enhancing the formation of electron pairs, leads to a repulsion between holes.
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.
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.