Physical review. B, Condensed matter

Frequency-dependent conductivity of the one-dimensional Hubbard model at strong coupling

Peter Horsch, W. Stephan

Published Oct 1, 1993• 28 citations

Abstract

The one-dimensional Hubbard model is characterized by charge-spin separation, but nevertheless in the doped system \ensuremath{\sigma}(\ensuremath{\omega}>0) does not vanish due to a small remaining coupling between charge and spin degrees of freedom. We derive an effective Hamiltonian and give in leading order (\ensuremath{\sim}${\mathit{J}}^{2}$) an analytic expression for \ensuremath{\sigma}(\ensuremath{\omega}) for the case of the Mott insulator doped with one hole. The complete frequency dependence in the strong-coupling limit of the Hubbard model and for the t-J model agrees with results from exact diagonalization. The limit \ensuremath{\sigma}(\ensuremath{\omega}\ensuremath{\rightarrow}0) at T=0 is found to be very different for the two models, i.e., \ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}^{3/2}$ in the strong-coupling limit and \ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{-}}1/2}$ for the t-J model.

DOI: 10.1103/physrevb.48.10595

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Physical review. B, Condensed matter

Frequency-dependent conductivity of the one-dimensional Hubbard model at strong coupling

Peter Horsch, W. Stephan

Published Oct 1, 1993• 28 citations

Publisher

Abstract

{\mathit{J}}^{2}

) an analytic expression for \ensuremath{\sigma}(\ensuremath{\omega}) for the case of the Mott insulator doped with one hole. The complete frequency dependence in the strong-coupling limit of the Hubbard model and for the t-J model agrees with results from exact diagonalization. The limit \ensuremath{\sigma}(\ensuremath{\omega}\ensuremath{\rightarrow}0) at T=0 is found to be very different for the two models, i.e., \ensuremath{\sim}

{\mathrm{\ensuremath{\omega}}}^{3/2}

in the strong-coupling limit and \ensuremath{\sim}

{\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{-}}1/2}

for the t-J model.

DOI: 10.1103/physrevb.48.10595

Related papers

Spin-charge decoupling and the Green’s function of one-dimensional Mott insulators

Alberto Parola, Sandro Sorella

An exact expression for the Green's function G(k,\ensuremath{\omega}) of one hole in the U\ensuremath{\rightarrow}\ensuremath{\infty} one-dimensional Hubbard model is derived from the known Bethe-ansatz solution of the model. Due to the spin-charge decoupling of the one-hole excitation spectrum and the Fermi-like statistics of the spin excitations, G shows branch-cut singularities at \ensuremath{\omega}=\ifmmode\pm\else\textpm\fi{}2 sink and a nontrivial dependence on the momentum of the hole. As a result, the hole can propagate although the quasiparticle weight vanishes.An exact expression for the Green's function G(k,\ensuremath{\omega}) of one hole in the U\ensuremath{\rightarrow}\ensuremath{\infty} one-dimensional Hubbard model is derived from the known Bethe-ansatz solution of the model. Due to the spin-charge decoupling of the one-hole excitation spectrum and the Fermi-like statistics of the spin excitations, G shows branch-cut singularities at \ensuremath{\omega}=\ifmmode\pm\else\textpm\fi{}2 sink and a nontrivial dependence on the momentum of the hole. As a result, the hole can propagate although the quasiparticle weight vanishes.

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{\mathit{J}}^{2}

{\mathrm{\ensuremath{\omega}}}^{3/2}

in the strong-coupling limit and \ensuremath{\sim}

{\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{-}}1/2}

for the t-J model.

U

and hence small exchange coupling

J

. The spin degrees of freedom are taken to be disordered. So we consider the limit $0<J\ensuremath{\ll}T\ensuremath{\ll}W$, where

W

is the bandwidth. We focus on evaluating the local spectral density of a single hole excitation and the charge gap that separates the upper and the lower Hubbard band. We find indications that no band edges exist if the magnetic exchange is taken into account; instead of band edges, Gaussian tails seem to appear. A discussion of the underlying physics is provided.

{\mathit{m}}^{\mathrm{*}}

of the quasiparticle and the frequency-dependent conductivity \ensuremath{\sigma}(\ensuremath{\omega}) are calculated for clusters with 4\ifmmode\times\else\texttimes\fi{}4 and 8\ifmmode\times\else\texttimes\fi{}4 sites. In particular, \ensuremath{\sigma}(\ensuremath{\omega}) shows an isolated quasiparticle peak of weak intensity at small \ensuremath{\omega} and a broad but structured incoherent part at higher \ensuremath{\omega}.

We study the strong correlation effects in the vicinity of the Mott metal-insulator transition using coupled clean or disordered Hubbard chains with a infinitely large coordinate number

D_{\perp}\to\infty

in the direction perpendicular to the chains and with a long-range transverse hopping. Strong electron correlation effects are treated partially non-perturbatively with the use of the exact results for the 1D Hubbard model. In the case of clean systems, the thermodynamic and transport quantities which characterize the Mott transition from the Fermi liquid state, such as the specific heat coefficient, the Drude weight, and the compressibility, are obtained as functions of hole-doping

δ=1-n

(

n

, electron density) by the systematic expansion in terms of the inverse of the transverse hopping range

l_{\perp}

. We find that the

δ

-dependence of these quantities shows non-universal behaviors with exponents depending on the strength of electron-electron interaction. In the presence of disorder, it is shown that the frequency-dependence of the dynamical conductivity obeys the Mott's law, implying the possibility of {\it Mott glass state} for

δ\to 0

, provided that there exists a finite range interaction.