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Physical review. B, Condensed matter

Instability of vortex textures in the two-dimensional Hubbard model

Kenji Yonemitsu, A. R. Bishop

Published Sep 1, 1993• 1 citation
Publisher

Abstract

The Hubbard model on a two-dimensional square lattice is investigated within an unrestricted, inhomogeneous Hartree-Fock approximation. Vortexlike states discussed by Verge\ifmmode\acute\else\textasciiacute\fi{}s et al. [Phys. Rev. B 43, 6099 (1991)] are studied in detail. They are found to be unstable against transverse spin fluctuations. Doping of holes does not suppress these fluctuations strongly enough to stabilize the vortex states.

DOI
10.1103/physrevb.48.6680

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The Hubbard model on a two-dimensional square lattice is investigated within an unrestricted, inhomogeneous Hartree-Fock approximation. Vortexlike states discussed by Verge\ifmmode\acute\else\textasciiacute\fi{}s et al. [Phys. Rev. B 43, 6099 (1991)] are studied in detail. They are found to be unstable against transverse spin fluctuations. Doping of holes does not suppress these fluctuations strongly enough to stabilize the vortex states.
The Hubbard model in a two-dimensional square lattice is studied within the unrestricted Hartree-Fock approximation. A wide variety of solutions are found, as a function of filling and value of the Coulomb repulsion. Their properties range from those of magnetic polarons to a behavior similar to electrons in an external magnetic field (flux phases). The main features of the vortex solution are studied. It is shown that its energy increases logarithmically with system size, and that it becomes more stable for high values of the Coulomb repulsion and doping levels. Also, multivortex configurations are shown to exist. The implications of our results in the qualitative behavior of the Hubbard model as function of doping and strength of the interaction are discussed.
Abstract The properties of a recently discovered unrestricted Hartree‐Fock solution of the Hubbard Hamiltonian is analysed on the square lattice that shows a really two‐dimensional spin polarization of a vortex‐like character. This and other several mean‐field solutions are compared with the exact ground‐state energy and wave function of two and four electrons on a four‐site system (square). Results for two correlated electrons in large 3 × 3 and 4 × 4 clusters are also given and discussed. The vortex mean‐field solution provides the best solution in almost all systems that deviate from half‐filling.
The homogeneous Hartree-Fock antiferromagnetic (AF) state of the doped Hubbard model is shown to be unstable for infinitesimal doping concentration. Driven by long-wavelength intraband fluctuations, this instability with respect to infinitesimal fluctuations around the mean-field state is inferred from the nature of the static spin response, which increases away from the AF wave vector (\ensuremath{\pi},\ensuremath{\pi}). The effective interaction between antiparallel-spin holes in the lower band is found to contain a short-range attractive component, with an energy scale Jx. We discuss the crossover of the characteristic length scale for intraband fluctuations from the antiferromagnetic state to the spiral state, also unstable for infinitesimal doping concentration.
We study the spin and charge textures of the two-dimensional Hubbard model for a wide range of electron filling at the ground state both on a square lattice and on a triangular lattice within a mean field approximation. We complete the overall phase diagram of the single-Q helical spin density wave state, which spreads widely in the electron filling and the Coulomb interaction plane, and discuss the relative stability of the soliton and the vortex lattice states on it. It is shown that the imperfect nesting condition, which is the intrinsic feature of two-dimensional systems, induces a rich variety of self-consistent solutions including collinear and noncollinear spin textures.
The internal structure of stripes in the two-dimensional Hubbard model is studied by going beyond the Hartree-Fock approximation. Partially filled stripes with inhomogeneous magnetization and charge along the stripe core, consistent with experimental observations, are stabilized by quantum fluctuations, included through the configuration interaction method. Similar configurations result to be stable for filled stripes, and have a lower energy than the standard paramagnetic core solution. Away from half-filling, solitonlike solutions show up within the Hartree-Fock approximation. The hopping of short regions of the stripes in the transverse direction is comparable to the bare hopping element. The hole-hole correlation shows maxima along the stripe direction, while the integrated value of ${n}_{\stackrel{\ensuremath{\rightarrow}}{k}}$ compares satisfactorily with experimental results.
We use a variational Monte Carlo technique to study the ground state of the two-dimensional Hubbard model on a square lattice. We study the stability of the usual commensurate antiferromagnetic phase against the formation of domain walls for various system sizes, band filling, and Hubbard repulsion. An instability towards diagonal domain walls is found for the values of the Hubbard repulsion studied (U=4-10t). We compute the condensation energy of the holes in walls. Such an incommensurate antiferromagnetic phase is much stabler than any other solution. Whether paramagnetic or purely superconducting, but superconductivity is found still to coexist with incommensurate antiferromagnetism. We carefully compare our results with those of the Hartree-Fock model and shed some light on the limitations of the Hartree-Fock solutions.