Numerical study of multisoliton configurations in a doped antiferromagnetic Mott insulator

Abstract

We evaluate from first principles the self-consistent Hartree-Fock energies for multisoliton configurations in a doped, spin-$\frac{1}{2}$, 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 $\ensuremath{\delta}=0.05$ 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 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 quasiparticle dispersion relations from that of a conventional AFM. The modified dispersion is consistent with angle-resolved photoemission studies and has a local minimum at wave vector $\stackrel{\ensuremath{\rightarrow}}{k}=\ensuremath{\pi}/2a(1,1)$, 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 midinfrared 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 $\stackrel{\ensuremath{\rightarrow}}{Q}=\ensuremath{\pi}/a(1,1)$, corresponding to the undoped AFM, splits into four satellite peaks that evolve with charge carrier concentration as observed experimentally. At very low doping $(\ensuremath{\delta}<0.05)$ the doping charges create extremely tightly bound meron-antimeron pairs or even isolated conventional spin polarons, whereas for very high doping $(\ensuremath{\delta}>0.4)$ 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.