We present a variational treatment of the ground state of the two-leg $t\ensuremath{-}J$ ladder, which combines the dimer and the hard-core boson models into one effective model. This model allows us to study the local structure of the hole pairs as a function of doping. A second-order recursion relation is used to generate the variational wave function, which substantially simplifies the computations. We obtain good agreement with numerical density matrix renormalization group results for the ground state energy in the strong-coupling regime. We find that the local structure of the pairs depends upon whether the ladder is slightly or strongly dopped.
Two-leg $t\ensuremath{-}J$ ladders are investigated in the framework of a combination of the phase string formulation and bond-operator representation. We develop a mean-field theory in the strong rung interaction regime, i.e., ${J}_{\ensuremath{\perp}}\ensuremath{\gg}J,t,$ which provides a unified description of the undoped insulating phase and the low-doping phase---the so-called
C1S0 phase. Both of them are characterized by the resonating-valence-bond (RVB) order parameter, with gap opened up in all spin excitations. The ground state of the doped phase is intrinsically a superconductor with a d-wave symmetry, which is driven by the RVB correlations. The ground-state energy is in good agreement with numerical results. Phase separation is shown to occur beyond some critical value of
J/t for given doping concentration. The local structure of hole pairs as well as the spectra of various spin and charge modes are analyzed in comparison with other approaches.
Holes weakly doped into a four-leg t-
J ladder bind in pairs. At dopings exceeding a critical doping of ${\ensuremath{\delta}}_{c}\ensuremath{\simeq}\frac{1}{8}$ four-hole clusters are observed to form in density-matrix renormalization-group calculations. The symmetry of the ground-state wave function does not change and we are able to reproduce this behavior qualitatively with an effective bosonic model in which the four-leg ladder is represented as two coupled two-leg ladders and hole pairs are mapped on hard-core bosons moving along and between these ladders. At lower dopings, $\ensuremath{\delta}<{\ensuremath{\delta}}_{c},$ a one-dimensional bosonic representation for hole pairs works and allows us to calculate accurately the Luttinger liquid parameter ${K}_{\ensuremath{\rho}}$ that takes the universal value ${K}_{\ensuremath{\rho}}=1$ as half-filling is approached.
Superconductivity is usually described in the framework of the Bardeen-Cooper-Schrieffer (BCS) wavefunction, which even includes the resonating-valence-bond (RVB) wavefunction proposed for the high-temperature superconductivity in the cuprate. A natural question is
if any fundamental physics could be possibly missed by applying such a scheme to strongly correlated systems. Here we study the pairing wavefunction of two holes injected into a Mott insulator/antiferromagnet in a two-leg ladder using variational Monte Carlo approach. By comparing with density-matrix renormalization group (DMRG) calculation, we show that a conventional BCS or RVB pairing of the doped holes makes qualitatively wrong predictions and is incompatible with the fundamental pairing force in the $t\text{\ensuremath{-}}J$ model, which is kinetic-energy driven by nature. By contrast, a non-BCS-like wavefunction incorporating such novel effect will result in a substantially enhanced pairing strength and improved ground state energy as compared to the DMRG results. We argue that the non-BCS form of such a new ground state wavefunction is essential to describe a doped Mott antiferromagnet at finite doping.
Based on three general guiding principles, i.e., no double occupancy constraint, accurate description of antiferromagnetism at half-filling, and the precise sign structure of the
t-
J model, a new ground state wave function has been constructed recently [Weng, New J. Phys. 13, 103039 (2011)]. In this paper, we specifically study such kind of variational ground state for the one-hole-doped anisotropic two-leg
t-
J ladder using variational Monte Carlo (VMC) method. The results are then systematically compared with those recently obtained by density matrix renormalization group (DMRG) simulation. An excellent agreement is found between the VMC and DMRG results, including a "quantum critical point" at the anisotropy parameter
α=αc≈0.7 (with the parameters
t/J=3), and the emergence of charge modulation and momentum (Fermi point) reconstruction at
α>αc due to the quantum interference of the sign structure. In particular, the wave function indicates that a Landau's quasiparticle description remains valid at
ααc due to the breakdown of the one-to-one correspondence of momentum and translational symmetry of the hole. The explicit form of the wave function provides a direct understanding on how the many-body strong correlation effect takes place non-perturbatively in a doped Mott insulator, which sheds interesting light on the two-dimensional case where the same type of wave function was proposed to describe the cuprate superconductor.