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arXiv:cond-mat/9701051 · Physical review. B, Condensed matter

Spectral functions of the one-dimensional Hubbard model in the U→+∞ limit:How to use the factorized wave function

Karlo Penc, K. Hallberg, Frédéric Mila, Hiroyuki Shiba

Published Jun 15, 1997• 91 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.55.15475

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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.
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The physics of the strongly interacting Hubbard chain (with $t/U\ensuremath{\ll}1$) at finite temperatures undergoes a crossover to a spin-incoherent regime when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale. This crossover can be understood by means of Ogata and Shiba's factorized wave function, where charge and spin are totally decoupled, and assuming that the charge remains in the ground state, while the spin is thermally excited and at an effective ``spin temperature.'' We use the time-dependent density matrix renormalization group method to calculate the dynamical contributions of the spin, to reconstruct the single-particle spectral function of the electrons. The crossover is characterized by a redistribution of spectral weight both in frequency and momentum, with an apparent shift by kF{k}_{F}kF​ of the minimum of the dispersion.
We have studied correlation functions of the one-dimensional Hubbard model using the density-matrix numerical renormalization-group approach. The singularity exponents of the momentum distribution at k=kF{\mathit{k}}_{\mathit{F}}kF​ and 3kF{\mathit{k}}_{\mathit{F}}kF​, as well as the power-law singularity of the spin-correlation function, are computed for large U (U/t=103{10}^{3}103). The momentum-distribution exponent at k=kF{\mathit{k}}_{\mathit{F}}kF​ and the spin-correlation exponent are in agreement with the analytic results, while the calculated exponent for momentum distribution at k=3kF{\mathit{k}}_{\mathit{F}}kF​ is about 3/4, which disagrees with the analytically predicted value 9/8. We also discuss several techniques for an accurate calculation of the correlation functions.