Numerical study of multisoliton configurations in a doped antiferromagnetic Mott insulator

Abstract

We evaluate from first principles the self-consistent Hartree-Fock energies for multi-soliton configurations in a doped, spin-1 2 , antiferromagnetic Mott insulator on a two-dimensional square lattice. The microscopic Hamiltonian for this system involves a nearest neighbor electron hopping matrix element t, an on-site Coulomb repulsion U , and a nearest neighbor Coulomb repulsion V . We find that nearest-neighbor Coulomb repulsion on the energy scale of t stabilizes a regime of charged meron-antimeron vortex soliton pairs over a region of doping from δ = 0.05 to 0.4 holes per site for intermediate coupling 3 ≤ U/t ≤ 8. This stabilization is mediated through the generation of "spin-flux" in the mean-field antiferromagnetic (AFM) background. Spin-flux is a new form of spontaneous symmetry breaking in a strongly correlated electron system in which the Hamiltonian acquires a term with the symmetry of spin-orbit coupling at the mean-field level. Spin-flux modifies the single quasi-particle dispersion relations from that of a conventional AFM. The modified dispersion is consistent with angle-resolved photo-emission studies and has a local minimum at wavevector k = π/2a(1, 1), where a is the lattice constant. Holes cloaked by a meron-vortex in the spin-flux AFM background are charged bosons. Our static Hartree-Fock calculations provide an upper bound on the energy of a finite density of charged vortices. This upper bound is lower than the energy of the corresponding charged spin-polaron configurations. A finite density of charge carrying vortices is shown to produce a large number of unoccupied electronic levels in the Mott-Hubbard charge transfer gap. These levels lead to significant band tailing and a broad mid-infrared band in the optical absorption spectrum as observed experimentally. In the presence of a finite density of charged meron-antimeron pairs, the peak in the magnetic structure at Q = π/a(1, 1), corresponding to the undoped AFM, splits into four satellite peaks which evolve with charge carrier concentration as observed experimentally. At very low doping (δ < 0.05) the doping charges create extremely tightly bound meron-antimeron pairs or even isolated conventional spin-polarons, whereas for very high doping (δ > 0.4) the spin background itself becomes unstable to formation of a conventional Fermi liquid and the spin-flux mean-field is energetically unfavorable. Our results point to the predominance of a quantum liquid of charged, bosonic, vortex solitons at intermediate coupling and intermediate doping concentrations.

A microscopic model for D-wave pairing in the cuprates: what happens when electrons somersault?

“…The doping hole is trapped in the core of a magnetic vortex, which indeed has azimuthal symmetry. The bound level on which the hole is trapped can be shown 18,14 to be split from the top of the valence band and drawn deep inside the Mott-Hubbard gap. As a result, the meronvortex is a charged boson.…”

“…An argument based on the electronic structure, identical to the one offered for the charged bosonic domain-walls of the polyacetylene, also holds. 17,18,14,20 The parallel to the quasi-one dimensional 1D polyacetylene is again a reflection of azimuthal symmetry which reduces the 2D continuum model to a 1D radial equation. Clearly, the isotropic dispersion about the Fermi points is responsible for the appearance of bosonic charge carriers.…”

Topological doping of repulsive Hubbard models

“…The question of the existence of meron-antimeron pairs in the ground state has been studied with various approaches [8,9,10]. The present situation is not satisfactory, since unrestricted Hartree-Fock calculations for the one-band Hubbard model have found meron-antimeron pair solutions, but never as the ground state [8].…”

“…Indeed, several authors propose that hole doping leads to the appearance of nontrivial structures of the surrounding Cu spins, such as dipolar configurations [1,7], vortices or merons [8,9,10], skyrmions [11,12,13], and domain walls or stripes [8,9,14,15,16].…”

“…This approach goes beyond the Hartree-Fock approximation (HFA) and leads to lower variational ground-state energies. Furthermore, in a one-band spin-flux model Berciu and John [10] also find meron-antimeron pairs as the ground state, employing the configuration-interaction (CI) method, which also goes beyond Hartree-Fock theory. Both approaches have not yet been applied to the three-band model.…”