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Physical review. B, Condensed matter

Flux states for the infinite-Ulimit of the Hubbard model

S. E. Barnes

Published Jul 1, 1991• 2 citations
Publisher

Abstract

For finite doping, \ensuremath{\delta}, relative to half filling, it is shown, within the confines of a mean-field auxiliary-operator formulation, for the strictly infinite-U, i.e., J=0, limit of the two-dimensional Hubbard model, that the spinons generate a fictitious magnetic flux to which holons are subject and vice versa. For small doping, a flux state is the absolute ground state and has 1-\ensuremath{\delta}=2p/q, where p/q is a rational fraction and the flux per plaquette is \ensuremath{\Phi}=(p/q)${\mathrm{\ensuremath{\Phi}}}_{0}$, where ${\mathrm{\ensuremath{\Phi}}}_{0}$ is the flux quantum. This phenomenon can be viewed upon as an all-electron Peierls instability or as broken statistical symmetry.

DOI
10.1103/physrevb.44.801

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arXiv:cond-mat/0105334•Physical review. B, Condensed matter•Jan 14, 2002•18 citations
For finite doping, \ensuremath{\delta}, relative to half filling, it is shown, within the confines of a mean-field auxiliary-operator formulation, for the strictly infinite-U, i.e., J=0, limit of the two-dimensional Hubbard model, that the spinons generate a fictitious magnetic flux to which holons are subject and vice versa. For small doping, a flux state is the absolute ground state and has 1-\ensuremath{\delta}=2p/q, where p/q is a rational fraction and the flux per plaquette is \ensuremath{\Phi}=(p/q)\ensuremathΦ0{\mathrm{\ensuremath{\Phi}}}_{0}\ensuremathΦ0​, where \ensuremathΦ0{\mathrm{\ensuremath{\Phi}}}_{0}\ensuremathΦ0​ is the flux quantum. This phenomenon can be viewed upon as an all-electron Peierls instability or as broken statistical symmetry.
We investigate certain generalized flux phases arising in a mean-field approach to the t-J model. First we establish that the energy of noninteracting electrons moving in a uniform magnetic field has an absolute minimum as a function of the flux at exactly one flux quantum per particle. Using this result we show that if the hard-core nature of the hole bosons is taken into account, then the generalized flux states in the mean-field approximation constitute a solution where both the spinons and the holons experience an average flux of one flux quantum per particle. We elaborate the relation to the integer and fractional quantum Hall effect. Based on this analogy one expects that only states with certain fractional fillings (ν=1/odd integer) are stable against the fluctuations of the (gauge) field. We speculate that at arbitrary fillings the system minimizes its energy by phase separating into these stable states. Finally we work out the ground state energy for nonuniform (staggered) flux phases and establish that the often claimed equivalence of frustration and doping does not hold for these states.
By utilizing the twisted boundary conditions in the exact diagonalization method, we investigate the single-particle spectral function of the extended Peierls-Hubbard model at both half-filling and quarter-filling. In one-dimensional (1D) interacting systems, the spin-charge separation can typically be identified in the single-particle spectral function by observing the distinct spinon and holon bands. At half-filling, starting from the pure 1D Hubbard model with the on-site interaction U=10U=10U=10, we observe that the band structure indicative of the spin-charge separation gradually transitions to four individual bands as the Peierls instability $\ensuremath{\delta}$ increases. At U=10U=10U=10 and $\ensuremath{\delta}=0.2$ where the spin-charge separation is still observable, increasing the nearest-neighbor interaction VVV can drive the system to a charge-density-wave state when $V\ensuremath{\gtrsim}U/2$. At quarter-filling, on the other hand, the ground state of Peierls-Hubbard model manifests an antiferromagnetic Mott insulator in units of dimers. Increasing UUU results in only a very small gap in the single-particle spectrum because even for $U=+\ensuremath{\infty}$, with the model transforming into a noninteracting half-filled dimerized tight-binding model, its gap determined by the Peierls instability $\ensuremath{\delta}$ remains small. Conversely, increasing VVV can effectively open the single-particle gap and make the spinon and holon bands more prominent.
We discuss the ground state magnetic phase diagram of the Hubbard model off half filling within the dynamical mean-field theory. The effective single-impurity Anderson model is solved by Wilson's numerical renormalization group calculations, adapted to symmetry broken phases. We find a phase separated, antiferromagnetic state up to a critical doping for small and intermediate values of U, but could not stabilize a Neel state for large U and finite doping. At very large U, the phase diagram exhibits an island with a ferromagnetic ground state. Spectral properties in the ordered phases are discussed.
The spin-holon effective Hamiltonian proposed by Zou and Anderson (1988) is used to calculate the chemical potential and the self-energy correction of spinons. The authors' results show that the effect of spin-exchange interaction is to enlarge the spinon bandwidth. For low temperatures and fixed doping fraction delta , the renormalized bandwidth and the chemical potential are nearly independent of temperature, but both change rapidly with the doping fraction. In the superfluid phase, the effect of increasing the doping fraction or increasing the on-site Coulomb repulsion U is to increase the relative kinetic energy of spinons, leading to a decrease in the superfluid transition temperature T s ( delta ), which is sensitive to various choices of U and the band parameter t; the increase in U tends to shift the boundary of T s ( delta ) towards a lower doping fraction. The correction due to spin fluctuations is extremely important for small doping fractions, leading to modification of the results of Baskaran, Zou and Anderson (1987), and Ruckstein, Hirschfeld and Appel (1987). Moreover, in the region of delta <or=8t/ pi 2 U, the effect of paramagnon fluctuations renders the mean-field theory invalid. The authors also discuss the effects of holon fluctuations on the mean-field results.