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.
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=10, we observe that the band structure indicative of the spin-charge separation gradually transitions to four individual bands as the Peierls instability
δ increases. At
U=10 and
δ=0.2 where the spin-charge separation is still observable, increasing the nearest-neighbor interaction
V can drive the system to a charge-density-wave (CDW) state when
V≳U/2, without the obeservation of spinon and holon bands. At quarter-filling, on the other hand, the ground state of Peierls-Hubbard model manifests an antiferromagnetic Mott insulator in units of dimers. Increasing
U results in only a very small gap in the single-particle spectrum because even for
U=+∞, with the model transforming into a noninteracting half-filled dimerized tight-binding model, its gap determined by the Peierls instability
δ remains small. Conversely, increasing
V can effectively open the single-particle gap and make the spinon and holon bands more prominent.
The one-dimensional extended Peierls-Hubbard model is studied at several band fillings using the density-matrix renormalization-group method. Results show that the ground state evolves from a Mott-Peierls insulator, with a correlation gap at half-filling, to a soliton lattice with a small band gap away from half-filling. It is also confirmed that the ground state of the Peierls-Hubbard model undergoes a transition to a metallic state at finite doping. These results show that electronic correlation effects should be taken into account in theoretical studies of doped polyacetylene. They also show that a Mott-Peierls theory could explain the insulator-metal transition observed in this material.
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=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=10 and $\ensuremath{\delta}=0.2$ where the spin-charge separation is still observable, increasing the nearest-neighbor interaction
V 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
U 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
V can effectively open the single-particle gap and make the spinon and holon bands more prominent.
We study the one-dimensional Holstein model with spin-
21 electrons at half filling. Ground-state properties are calculated for long chains with great accuracy using the density-matrix renormalization-group method and extrapolated to the thermodynamic limit. We show that for small electron-phonon coupling or large phonon frequency, the insulating Peierls ground state predicted by mean-field theory is destroyed by quantum lattice fluctuations and that the system remains in a metallic phase with a nondegenerate ground state and power-law electronic and phononic correlations. When the electron-phonon coupling becomes large or the phonon frequency small, the system undergoes a transition to an insulating Peierls phase with a twofold degenerate ground state, long-range charge-density-wave order, a dimerized lattice structure, and a gap in the electronic excitation spectrum.
The adiabatic Holstein-Hubbard model describes electrons on a chain with step a interacting with themselves (with coupling U) and with a classical phonon field ${\ensuremath{\varphi}}_{x}$ (with coupling \ensuremath{\lambda}). There is Peierls instability if the electronic ground-state energy $F(\ensuremath{\varphi})$ as a functional of ${\ensuremath{\varphi}}_{x}$ has a minimum which corresponds to a periodic function with period $\ensuremath{\pi}{/p}_{F},$ where
pF is the Fermi momentum. We consider ${p}_{F}/\ensuremath{\pi}a$ irrational so that the charge-density wave is incommensurate with the chain. We prove in a rigorous way in the spinless case, when \ensuremath{\lambda}, U are small and $U/\ensuremath{\lambda}$ large, that (a) when the electronic interaction is attractive
U<0 there is no Peierls instability and (b) when the interaction is repulsive
U>0 there is Peierls instability in the sense that our convergent expansion for $F(\ensuremath{\varphi}),$ truncated at second order has a minimum which corresponds to an analytical and $\ensuremath{\pi}{/p}_{F}$ periodic ${\ensuremath{\varphi}}_{x}.$ Such a minimum is found solving an infinite set of coupled self-consistent equations, one for each of the infinite Fourier modes of ${\ensuremath{\varphi}}_{x}.$