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arXiv:cond-mat/9312049 · Physical Review Letters

Spectral Properties of the One-Dimensional Hubbard Model

R. Preuss, A. Muramatsu, Wolfgang von der Linden, Peter Dieterich, Fakher F. Assaad, Werner R. Hanke

Published Aug 1, 1994• 83 citations
arXivHTMLPDF

Abstract

The spectral properties of the 1D Hubbard model are obtained from quantum Monte Carlo simulations on large systems ($N=84$) using the maximum entropy method. It is shown for the first time that the one-particle excitations are characterized by dispersive cosinelike bands, in extremely good agreement with slave-boson mean-field ones. Velocities for spin and charge excitations are obtained that lead to a conformal charge $c=0.98\ifmmode\pm\else\textpm\fi{}0.05$. An exact sum rule for spin and charge excitations is fulfilled accurately with deviations of at most 10% only around $2{k}_{F}$.

DOI
10.1103/physrevlett.73.732

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The spectral properties of the 1D Hubbard model are obtained from quantum Monte Carlo simulations on large systems (N=84N=84N=84) using the maximum entropy method. It is shown for the first time that the one-particle excitations are characterized by dispersive cosinelike bands, in extremely good agreement with slave-boson mean-field ones. Velocities for spin and charge excitations are obtained that lead to a conformal charge c=0.98\ifmmode±\else\textpm\fi0.05c=0.98\ifmmode\pm\else\textpm\fi{}0.05c=0.98\ifmmode±\else\textpm\fi0.05. An exact sum rule for spin and charge excitations is fulfilled accurately with deviations of at most 10% only around 2kF2{k}_{F}2kF​.
We investigate the dynamical properties of the one-dimensional Hubbard model using the quantum Monte Carlo method and the numerical analytic continuation method based on the maximum entropy principle. Results for the spin, charge and current excitation spectrum are presented for various values of the coupling and the band filling for the system of 24 sites with the periodic boundary condition. We find that the total spectral density of the spin excitation exhibits a gapless structure irrespective of the coupling or the band filling. The charge excitation spectrum, on the other hand, clearly shows the gap formation at the half filled band and shifts its weight toward the higher energy region with increase of the coupling. This charge excitation gap, however, disappears with the hole doping. We also discuss the momentum dependence of the spectral functions.
Using grand canonical quantum Monte Carlo (QMC) simulations combined with maximum entropy analytic continuation, as well as analytical methods, we examine the one- and two-particle dynamical properties of the Hubbard model on two coupled chains at half-filling. The one-particle spectral weight function, A(k,\ensuremath{\omega}), undergoes a qualitative change with interchain hopping ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ associated with a transition from a four-band insulator to a two-band insulator. A simple analytical model based on the propagation of exact rung singlet states gives a good description of the features at large ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$. For smaller ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$, A(k,\ensuremath{\omega}) is similar to that of the one-dimensional model, with a coherent band of width the effective antiferromagnetic exchange J which is reasonably well described by renormalized spin-wave theory. The coherent band rides on a broad background of width several times the parallel hopping integral t, an incoherent structure similar to that found in calculations on both the one- and two-dimensional models. We also present QMC results for the two-particle spin and charge excitation spectra, and relate their behavior to the rung singlet picture for large ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ and to the results of spin-wave theory for small ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$. \textcopyright{} 1996 The American Physical Society.
The problem of spin-charge separation is analyzed numerically in the metallic phase of the one-band Hubbard model in one dimension by studying the behavior of the single-particle Green's function and of the spin and charge susceptibilities. We first analyze the quantum Monte Carlo data for the imaginary-time Green's function within the maximum-entropy method in order to obtain the spectral function at real frequencies. For some values of the momentum sufficiently away from the Fermi surface two separate peaks are found, which can be identified as charge and spin excitations. In order to improve our accuracy and to be able to extend our study to a larger portion of the Brillouin zone, we also fit our data with the imaginary-time Green's function obtained from the Luttinger-model solution with two different velocities as fitting parameters. The excitation energies associated with these velocities turn out to agree, in a broad range of momenta, with the ones calculated from the charge and spin susceptibilities. This allows us to identify these single-particle excitations as due to a separation of spin and charge. Remarkably, the range of momenta where spin-charge separation is seen extends well beyond the region of linear dispersion about the Fermi surface. We finally discuss a possible extension of our method to detect spin-charge separation numerically in two dimensions.
Dynamic properties of the three-dimensional single-band Hubbard model are studied using quantum Monte Carlo combined with the maximum entropy technique. At half-filling, there is a clear gap in the density of states and well-defined quasiparticle peaks at the top (bottom) of the lower (upper) Hubbard band. We find an antiferromagnetically induced weight above the naive Fermi momentum. Upon hole doping, the chemical potential \ensuremath{\mu} moves to the top of the lower band where a robust peak is observed. Results are compared with spin-density-wave mean-field and self-consistent Born approximation results, and also with the infinite-dimensional (D=\ensuremath{\infty}) Hubbard model, and experimental photoemission for three-dimensional transition-metal oxides. \textcopyright{} 1996 The American Physical Society.
We give the details of the calculation of the spectral functions of the one-dimensional Hubbard model using the spin-charge factorized wave function for several versions of the U\ensuremath{\rightarrow}+\ensuremath{\infty} limit. The spectral functions are expressed as a convolution of charge and spin dynamical correlation functions. A procedure to evaluate these correlation functions very accurately for large systems is developed, and analytical results are presented for the low-energy region. These results are fully consistent with the conformal field theory. We also propose a direct method of extracting the exponents from the matrix elements in more general cases.