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Physical review. B, Condensed matter

Superconducting correlations in the one-dimensionalt-Jmodel

Thomas Pruschke, Hiroyuki Shiba

Published Jul 1, 1992• 14 citations
Publisher

Abstract

The t-J model is the simplest Hamiltonian for strongly correlated electrons, in which a superconducting phase may be present. This paper discusses superconducting correlation functions of the one-dimensional t-J model obtained from exact diagonalization of finite systems. Singlet and triplet channels are examined and compared with each other; the results are interpreted in terms of the Luttinger-liquid theory. A detailed study is made of the small-J limit, where the special form of the ground-state wave function allows a thorough study of correlation functions, including logarithmic corrections to the leading power-law decay. In addition, the effect of a magnetic field is also examined, since singlet and triplet superconducting correlations are competitive at zero field. It turns out that the magnetic field modifies the superconducting correlations in an interesting way. In particular, an analog of the Fulde-Ferrell state is found for some intermediate J.

DOI
10.1103/physrevb.46.356

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Advanced series in mathematical physics•May 1, 1994•0 citations
The t-J model is the simplest Hamiltonian for strongly correlated electrons, in which a superconducting phase may be present. This paper discusses superconducting correlation functions of the one-dimensional t-J model obtained from exact diagonalization of finite systems. Singlet and triplet channels are examined and compared with each other; the results are interpreted in terms of the Luttinger-liquid theory. A detailed study is made of the small-J limit, where the special form of the ground-state wave function allows a thorough study of correlation functions, including logarithmic corrections to the leading power-law decay. In addition, the effect of a magnetic field is also examined, since singlet and triplet superconducting correlations are competitive at zero field. It turns out that the magnetic field modifies the superconducting correlations in an interesting way. In particular, an analog of the Fulde-Ferrell state is found for some intermediate J.
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.
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.
We analyze superconducting correlations in the one-dimensional Kondo lattice models with Ising anisotropy under transverse magnetic fields, using the density matrix renormalization group. For the spin-1/2 local spin model, the Ising anisotropy is introduced by the ferromagnetic Ising interaction between the local spins, while for the spin-1 model, it is taken by the single-ion anisotropy. The magnetic properties under the transverse fields for the spin-1/2 model are very similar to those for the spin-1 model [K. Suzuki and K. Hattori, J. Phys. Soc. Jpn. 88, 024707 (2019).]. For the superconducting correlations, we analyze various Cooper pairs within nearest-neighbor pairs including composite ones between the local spins and the electrons. We find that, for the spin-1/2 model, the superconducting correlations are highly enhanced in the Tomonaga-Luttinger liquid state near the Kondo-plateau phase, where the conduction electrons and the local spins are strongly coupled with a finite spin gap for the Ising axis. This is a clear contrast to the model under the longitudinal magnetic fields, where there are no noticeable superconducting correlations. Competitions between the transverse magnetic field and the Kondo singlet formation lead to this enhanced superconducting correlations. For the spin-1 model, the single-ion anisotropy suppresses the superconducting correlation and there is no noticeable enhancement. We also examine the large Kondo exchange coupling limit. For the moderate ferromagnetic Ising interaction between the local spins, we find that another type of superconducting correlation is enhanced inside the ferromagnetic phase. We discuss a possible relation between our results and reentrant superconductivity in U-based ferromagnetic superconductors under transverse magnetic fields.
An exact description is given of the long-distance behaviour of the one-dimensional t-J model at t=J. The authors employ the Bathe ansatz method and the finite-size scaling technique in conformal field theory. The charge and spin degrees of freedom are separated, and described by two independent c=1 conformal theories. The critical exponents for the charge, spin, electron and superconducting correlation functions are obtained for arbitrary band filling. The authors then make detailed comparison of the t-J model with the repulsive Hubbard model with emphasis on the Luttinger liquid properties. Analysing the electron filling dependence they observe the enhancement of the superconducting correlations compared with the highly correlated Hubbard model. The effect of the external magnetic field at and near half-filling is also discussed.
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.
An exact description is given of the long-distance behaviour of the one-dimensional t-J model at t=J. The authors employ the Bathe ansatz method and the finite-size scaling technique in conformal field theory. The charge and spin degrees of freedom are separated, and described by two independent c=1 conformal theories. The critical exponents for the charge, spin, electron and superconducting correlation functions are obtained for arbitrary band filling. The authors then make detailed comparison of the t-J model with the repulsive Hubbard model with emphasis on the Luttinger liquid properties. Analysing the electron filling dependence they observe the enhancement of the superconducting correlations compared with the highly correlated Hubbard model. The effect of the external magnetic field at and near half-filling is also discussed.