We analytically calculate the ground state pairing symmetry and excitation spectra of two holes doped into the half-filled t-t'-t''-J_z model in the strong-coupling limit (J_z >> |t|, |t'|, |t''|). For the t'-t''-J_z model, there are regions of d-wave, s-wave, and p-wave symmetry. We find that the t-J_z model maps in lowest order onto the t'-t''-J_z model on the boundary between d and p symmetry, with a flat lower branch of the pair excitation spectrum. In higher order d-wave symmetry is selected; however, we predict that the addition of the appropriate t' and/or t'' should drive the hole-pair symmetry to p-wave. We perturbatively construct an extended quasi-pair for the t-J_z model. We compare with analytic calculations for a 2x2 plaquette and numerical work, and discuss implications for the experimentally relevant parameter regime.
We analytically calculate the ground state pairing symmetry and excitation spectra of two holes doped into the half-filled t-t'-t''-J_z model in the strong-coupling limit (J_z >> |t|, |t'|, |t''|). For the t'-t''-J_z model, there are regions of d-wave, s-wave, and p-wave symmetry. We find that the t-J_z model maps in lowest order onto the t'-t''-J_z model on the boundary between d and p symmetry, with a flat lower branch of the pair excitation spectrum. In higher order d-wave symmetry is selected; however, we predict that the addition of the appropriate t' and/or t'' should drive the hole-pair symmetry to p-wave. We perturbatively construct an extended quasi-pair for the t-J_z model. We compare with analytic calculations for a 2x2 plaquette and numerical work, and discuss implications for the experimentally relevant parameter regime.
We analytically calculate the ground state pairing symmetry and excitation spectra of two holes doped into the half-filled $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}\ensuremath{-}{J}_{z}$ model in the strong-coupling limit $({J}_{z}⪢\ensuremath{\mid}t\ensuremath{\mid},\ensuremath{\mid}{t}^{\ensuremath{'}}\ensuremath{\mid},\ensuremath{\mid}{t}^{\ensuremath{''}}\ensuremath{\mid})$. In leading order, this reduces to the ${t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}\ensuremath{-}{J}_{z}$ model, where there are regions of d-wave, s-wave, and (degenerate) p-wave symmetry. We find that the $t\ensuremath{-}{J}_{z}$ model maps in lowest order onto the ${t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}\ensuremath{-}{J}_{z}$ model on the boundary between d and p symmetry, with a flat lower band in the pair excitation spectrum. In higher order, d-wave symmetry is selected from the lower pair band. However, we observe that the addition of the appropriate ${t}^{\ensuremath{'}}<0$ and/or ${t}^{\ensuremath{''}}>0$, the signs of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ found in the hole-doped cuprates, could drive the hole-pair symmetry to p-wave symmetry, implying the possibility of competition between p-wave and d-wave pair ground states. (An added ${t}^{\ensuremath{'}}>0$ and/or ${t}^{\ensuremath{''}}<0$ generally tend to promote d-wave symmetry.) We perturbatively construct an extended quasipair for the $t\ensuremath{-}{J}_{z}$ model. In leading order, there are contributions from sites at a distance of 2 lattice spacings apart; however, contributions from sites two lattice spacings apart, also of the same order, vanish identically. Finally, we compare our approach with analytic calculations for a $2\ifmmode\times\else\texttimes\fi{}2$ plaquette and with existing numerical work, and discuss possible relevance to the physical parameter regime.
We study dynamical properties of two holes in the t-J, t-Jz, and Hubbard models using exact diagonalization techniques on small clusters. For the three models we found that the ground state of two holes has d-wave symmetry. Studying the dynamical d-wave pairing susceptibility at zero momentum, we observed a quasiparticle-like peak at the bottom of the spectrum in a broad region of parameter space. The lowest-energy p-wave state is close in energy to the d-wave ground state, and they both behave qualitatively similarly, while the lowest-energy states of the s-wave and extended-s-wave subspaces have higher energies and present no quasiparticle peak. The ground-state energy of two holes in the t-J model scales with J as a power law. Binding energies for different symmetries as well as dynamical properties for nonzero momentum are also discussed.
The $t\ensuremath{-}{J}_{z}$ model is the strongly anisotropic limit of the $t\ensuremath{-}J$ model which captures some general properties of doped antiferromagnets (AF's). The absence of spin fluctuations simplifies the analytical treatment of hole motion in an AF background, and allows us to calculate single- and two-hole spectra with a high accuracy using a regular diagram technique combined with a real-space approach. At the same time, numerical studies of this model via exact diagonalization on small clusters show negligible finite-size effects for a number of quantities, thus allowing a direct comparison between analytical and numerical results. Both approaches demonstrate that the holes have a tendency to pair in p- and d-wave channels at realistic values of t/J. Interactions leading to pairing and effects selecting p and d waves are thoroughly investigated. The role of transverse spin fluctuations is considered using perturbation theory. Based on the results of the present study, we discuss the pairing problem in the realistic $t\ensuremath{-}J$-like model. Possible implications for preformed pairs formation and phase separation are drawn.
A two-chain ladder model is considered that is described by the strong-coupling t - t ´- J - J ´ Hamiltonian. For the case of two holes moving in a background of antiferromagnetically interacting spins, exact, analytical results are derived for the ground-state energy and low-lying excitation spectrum. The ground state is a bound state of two holes with total spin S = 0. The charge excitation is gapless and the spin excitation has a gap. The corresponding wave functions are also exactly determined. The bound hole pair is found to have symmetry of the d-wave type. In the limit of strong rung coupling, the model maps onto an effective hard-core-boson model which exhibits dominant superconducting pairing correlations.
A single-hole ground state Ansatz for the two-dimensional t-J model has been recently studied by the variational Monte Carlo (VMC) method.Such a doped hole behaves like a "twisted" non-Landau quasiparticle characterized by an emergent quantum number in agreement with exact numerics.In this work, we further investigate the ground state of two holes by VMC.It is found that the two holes strongly attract each other to form a pairing state with a new quantum number the same as obtained by the numerical exact diagonalization and density matrix renormalization group (DMRG) calculations.A unique feature of this pairing state is a dichotomy in the pairing symmetry, i.e., a d wave in terms of the electron c operators and an s wave in terms of the new quasiparticles, as explicitly illustrated in the ground state wave function.A similar VMC study of a two-hole wave function for the t-J two-leg ladder also yields a good agreement with the DMRG result.We demonstrate that the pairing mechanism responsible for the strong binding here is not due to the long-range antiferromagnetic order nor the resonating-valence-bound pairing in the spin background but is the consequence of the quantum phase strings created by the hopping of holes.The resulting spin-current pattern mediating the pairing force is explicitly illustrated in the VMC calculation.Physical implications to superconductivity at finite doping are also discussed.
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 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(Q) also behaves as 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 cuprates.