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arXiv:cond-mat/9807027 · Physical Review Letters

d -Wave Pairing Correlation in the Two-Dimensional t−J Model

C. T. Shih, Y. C. Chen, Hua Lin, T. K. Lee

Published Aug 10, 1998• 47 citations
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Abstract

The pair-pair correlation function of the two-dimensional $t\ensuremath{-}J$ model is studied by using the power-Lanczos method under the assumption of monotonic behavior. In comparison with the results of the ideal Fermi gas, we conclude that the 2D $t\ensuremath{-}J$ model does not have long-range $d$-wave superconducting correlation in the interesting parameter range of $J/t\ensuremath{\le}0.5$. Implications of this result are also discussed.

DOI
10.1103/physrevlett.81.1294

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Physical review. B, Condensed matter•Apr 15, 1997•4 citations
The pair-pair correlation function of the two-dimensional t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model is studied by using the power-Lanczos method under the assumption of monotonic behavior. In comparison with the results of the ideal Fermi gas, we conclude that the 2D t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model does not have long-range ddd-wave superconducting correlation in the interesting parameter range of J/t\ensuremath≤0.5J/t\ensuremath{\le}0.5J/t\ensuremath≤0.5. Implications of this result are also discussed.
We reported that the pair-pair correlation function of the two-dimensional t-J model does not have long-range d-wave superconducting correlations in the interesting parameter range of J/t≤0.5J/t \leq 0.5J/t≤0.5. The power-Lanczos method is used under the assumption of monotonic behavior. This assumption has been well checked in the two-dimensional t-J and attractive Hubbard model. Here we re-examine this criterion of monotonic behavior of the pairing correlation function for the one-dimensional and two-leg t-J ladder where other accurate numerical results are available. The method seems to be working well.
The d-wave pair-pair correlation of the two-dimensional Hubbard model is investigated by the power-Lanczos method. A Jastrow-BCS type wave function is used in our variational study. By assuming a monotonic behavior of the long-range pairing correlation under Lanczos iteration, we found there is no long-range pairing order in the intermediate interaction region (U ≃ 10), which is consistent with the former result by the constrained-path Monte Carlo method. We also present numerical results obtained by the exact diagonalization of the 4×4 lattice in supporting our conclusion. PACS numbers: 74.20.-z, 71.18.+y I.
The two-dimensional t-J model in the ground state is investigated by the power Lanczos method. The pairing-pairing correlation function for ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$-wave symmetry is enhanced in the realistic parameter regime for high-Tc{\mathrm{T}}_{\mathrm{c}}Tc​ superconductors. The charge susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{c}}$ shows divergent behavior as ${\mathrm{\ensuremath{\chi}}}_{\mathrm{c}}$\ensuremath{\propto}${\mathrm{\ensuremath{\delta}}}^{\mathrm{\ensuremath{-}}1}$ near half filling for the doping concentration \ensuremath{\delta}, indicating that the value of the dynamical exponent z is four under the assumption of hyperscaling. The peak height of the spin structure factor Smax{\mathrm{S}}_{\mathrm{max}}Smax​(Q) also behaves as Smax{\mathrm{S}}_{\mathrm{max}}Smax​(Q)\ensuremath{\propto}${\mathrm{\ensuremath{\delta}}}^{\mathrm{\ensuremath{-}}1}$ near half filling, which leads to the divergence of the antiferromagnetic correlation length ${\ensuremath{\xi}}_{\mathrm{m}}$ as ${\ensuremath{\xi}}_{\mathrm{m}}$\ensuremath{\propto}${\mathrm{\ensuremath{\delta}}}^{\mathrm{\ensuremath{-}}1\mathrm{/}2}$. The boundary of phase separation is estimated on the basis of the Maxwell construction. Numerical results are compared with experimental features observed in high-Tc{\mathrm{T}}_{\mathrm{c}}Tc​ cuprates.
In this paper, the effect of the next-earest (t ′ ) and third-earest (t ′ ′ ) hopping terms on superconductivity (SC) of the two-dimensional (2D) extended t-J model is studied by the variational Monte-Carlo (VMC) method. For hole-doped systems, the d-wave pairing correlation is suppressed by t ′ and t ′ ′ for underdoped cases, while it can be greatly enhanced by proper values of t ′ and t ′ ′ for the overdoped ones. This behavior results from the deformation of the Fermi surfaces. PACS numbers: 74.20.-z, 71.18.+y The 2D t-J model is one of the most popular models for studying the properties of the high-temperature superconductivity (HTS) [1, 2]. Yet the problem whether this model can give such high Tc for the cuprates or not is still under debate [4–7]. It has been well accepted that the next-nearest-neighbor (t ′ ) and the third-nearest-neighbor (t ′ ′) hopping terms are necessary for models to explain several experiments like angle-resolved photoemission (ARPES) of HTS [3]. However, the effect of t ′ and t ′ ′ on pairing correlation is also controversial. Previous DMRG studies of the two-dimensional (2D) extended t-J model show that the SC is suppressed (enhanced) for negative (positive) next-nearestneighbor hopping t ′ /t [8]. But results from first-principle calculation show that t ′ /t = −0.3 maximizes SC at optimal doping [9]. The Hamiltonian of the extended t-J model is H = Ht + HJ = − ∑ ij tij(˜c † i,σ ˜cj,σ + H.C.) + J ∑
The spin, charge and pairing correlation functions for the ground state of two-dimensional t−Jt-Jt−J model are calculated by using the power method which projects out the ground state from a variational wave function. ``Exact'' results are obtained for 10×1010\times1010×10 and 8×88\times88×8 lattices with low particle densities. The results are surprisingly similar to that of one-dimensional t−Jt-Jt−J model. The phenomenology is almost perfectly correlated with the concept of Tomonaga-Luttinger liquid and it is incompatible with traditional Fermi liquid theory.
The two-dimensional Hubbard model near half-filling is studied using a configuration-interaction method. Superconducting order-parameter and spin-spin correlation functions are calculated as functions of distance to probe for superconductivity and antiferromagnetism. Consistent with our previous results, these more extensive calculations point toward d-wave superconductivity in the ground state of the two-dimensional repulsive Hubbard model. The d-wave correlations tend to increase with interaction strength, size of the state space used in the calculation, and doping away from half-filling. The superconducting correlations on the Fermi surface are interpreted as d-wave pairing between spin density-wave quasiparticles.