Two-hole Ground State Research Articles

Two-Hole Ground State: Dichotomy in Pairing Symmetry

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.

Hidden spin current in doped Mott antiferromagnets

We investigate the nature of doped Mott insulators using exact diagonalization and density matrix renormalization group methods. Persistent spin currents are revealed in the ground state, which are concomitant with a nonzero total momentum or angular momentum associated with the doped hole. The latter determines a nontrivial ground state degeneracy. By further making superpositions of the degenerate ground states with zero or unidirectional spin currents, we show that different patterns of spatial charge and spin modulations will emerge. Such anomaly persists for the odd numbers of holes, but the spin current, ground state degeneracy, and charge/spin modulations completely disappear for even numbers of holes, with the two-hole ground state exhibiting a d-wave symmetry. An understanding of the spin current due to a many-body Berry-like phase and its impact on the momentum distribution of the doped holes will be discussed.

D x2– y2 pairing in the generalized Hubbard square-lattice model

The pairing between holes in a square lattice and the two-particle wave-function symmetry are studied within a generalized Hubbard model. The key participation of the next-nearest-neighbor correlated-hopping interaction in the appearance of d-wave two-hole ground state is found, which is enhanced by the on-site repulsive Coulomb interaction. There is a clear pairing asymmetry between electrons and holes, where the hole pairing occurs in a realistic regime of interactions. The two-particle states are analyzed by looking at the binding energy, the coherence length, and the effective mass of the pairs. Finally, the case of a hole-singlet in an antiferromagnetic background is also studied.

Comparison of the π and Δ operator approximations for the two-dimensional t– J model

We compare the spectra of the new π operator of the SO(5) theory and the conventional Δ operator for the two-dimensional t– J model. We also calculate the weight transferred to the two-hole ground state from half-filling by these operators. We find that the spectra of these operators are quite similar and the weight for the π operator is smaller than the weight for the Δ operator. We argue that the two-dimensional t– J model does not have a good approximate SO(5) symmetry claimed in Ref. [1].

Spin excitons — a new mechanism of superconducting pairing in copper oxides

The Fermi and Bose quasiparticle spectrum in copper oxides is studied in a many-band p-d model taking account of the strong electronic correlations. It is shown that hole-doped systems possess a Bose mode — a spin exciton — which is associated with the singlet-triplet excitation of the two-hole ground-state term of CuO4 clusters. Intercluster hopping leads to fermion-boson interaction with a spin exciton as the intermediate boson. Such a mechanism does not exist for n-type systems.

Approximations to the two-hole ground state of the Hubbard-Anderson model: a numerical test

Several resonating-valence-bond-type states are being considered as an approximation of the two-hole ground state of the two-dimensional Hubbard-Anderson model. These states have been carefully constructed by Traa and Caspers with such algebraic properties, as to optimise different contributions of the Hubbard-Anderson hamiltonian. In this paper, the different contributions to their energies are calculated for lattices with sizes from 8 × 8 up to 16 × 16 and periodic boundary conditions, using a variational Monte-Carlo method. We show which state is lowest in energy and, more important, why this is so. In accordance with the optimal state from this tested set, we propose a bound state. It will be shown that this state is indeed the most stable state.

The two-hole ground state of the Hubbard-Anderson model, approximated by a variational RVB-type wave function

In this paper the Hubbard-Anderson model on a square lattice with two holes is studied. The ground state (GS) is approximated by a variational RVB-type wave function. The holes interact by exchange of a localized spin excitation (SE), which is created or absorbed if a hole moves to a nearest-neighbour site. An SE can move over the sublattice on which it is created. A variational calculation of the GS and the GS-energy is performed for an open-ended 4 × 4 lattice with two holes with the restriction that the SE is neighbouring both holes and does not move over its sublattice. It is found that the two holes prefer a bound state in which their mutual distance is 1 or 2 (with lattice spacing 1).

Binding of holes and the pair spectral function in the t-J model.

Clusters of the two-dimensional t-J model with two holes and up to 26 sites are diagonalized using a Lanczos algorithm. The behavior of the binding energy with system size suggests the existence of a finite critical value of J above which binding occurs in the bulk. Only the d-wave pair-field operator acting on the Heisenberg ground state has a finite overlap with the two-hole ground state for all the clusters considered. The related spectral function associated with the propagation of a d-wave (singlet) pair of holes in the antiferromagnetic background is calculated. The quasiparticle peak at the bottom of the spectrum as well as some structure appearing above the peak survive with increasing cluster size. Although no simple scaling law was found for the quasiparticle weight the data strongly suggest that this weight is finite in the bulk limit and is roughly proportional to the antiferromagnetic coupling J (for J1).

Holes in the infinite-U Hubbard model: Instability of the Nagaoka state.

The solution of a three-body Schr\"odinger equation (for two holes and a spin flip) shows that in the U=\ensuremath{\infty} Hubbard model the saturated ferromagnetic state with two holes is unstable (in a finite volume and for periodic boundary conditions). The ground state carries a finite momentum, and becomes degenerate with the Nagaoka state in the thermodynamic limit. This is in agreement with exact diagonalization results for small lattices where, in addition, we find that the true two-hole ground state is a singlet. As a result, our notions of ferromagnetism in the Hubbard model might need revision.