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arXiv:cond-mat/9705094 · Progress of Theoretical Physics

The Effect of Thermal Fluctuation on Spectral Function for the Tomonaga-Luttinger Model

N. Nakamura, Yoshikazu Suzumura

Published Jul 1, 1997• 16 citations
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Abstract

We examine the spectral function of the single electron Green function at finite temperature for the Tomonaga-Luttinger model which consists of a mutual interaction with only forward scattering. The spectral weight, which is calculated as a function of the frequency with fixed wave number, shows that several peaks originating in the excitation spectra of charge and spin fluctuations merge into a single peak by the increase of temperature.

DOI
10.1143/ptp.98.29

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We examine the spectral function of the single electron Green function at finite temperature for the Tomonaga-Luttinger model which consists of a mutual interaction with only forward scattering. The spectral weight, which is calculated as a function of the frequency with fixed wave number, shows that several peaks originating in the excitation spectra of charge and spin fluctuations merge into a single peak by the increase of temperature.
Using the functional integral bosonization technique, the spinless Tomonaga - Luttinger model with impurity forward scattering is solved exactly. Explicit analytical results are given for the one- and two-particle spectral functions in terms of a convolution integral representation. Sharp structures in the frequency spectra of an ordered system are smoothed out by the disorder. The existence of a charge - density instability is predicted if the critical exponent is less than -0.5. There is no influence of the disorder on the superconducting spectral function .
We use bosonization methods to calculate the exact finite-temperature single-electron Green's function of a spinful Luttinger liquid confined by open boundaries. The corresponding local spectral density is constructed and analyzed in detail. The interplay between boundary, finite-size, and thermal effects are shown to dramatically influence the low-energy properties of the system. In particular, the well-known zero-temperature critical behavior in the bulk always crosses over to a boundary dominated regime in the vicinity of the Fermi level. Thermal fluctuations cause an enhanced depletion of spectral weight for small energies $\ensuremath{\omega}$, with the spectral density scaling as ${\ensuremath{\omega}}^{2}$ for $\ensuremath{\omega}$ much less than the temperature. Consequences for photoemission experiments are discussed.
We calculate the finite temperature single-hole spectral function and the spin dynamic structure factor of a spinful one-dimensional Tomonaga-Luttinger liquid. Analytical expressions are obtained for a number of special cases. We also calculate the single-hole spectral function of a spin-gapped Luther -Emery liquid and obtain exact results at the free-fermion point K s = ½ These results may be applied to the analysis of angle-resolved photoemission and neutron scattering experiments on quasi-one-dimensional materials.
We examine zero-temperature one-particle spectral functions for the one-dimensional two-band spinless fermions with different velocities and general forward-scattering interactions. By using the bosonization technique and diagonalizing the model to two Tomonaga-Luttinger liquid Hamiltonians, we obtain general expressions for the spectral functions, which are given in terms of the Appell hypergeometric functions. For the case of identical two-band fermions, corresponding to the SU(2) symmetric spin-1/2 fermions with repulsive interactions, the spectral functions can be expressed in terms of the Gauss hypergeometric function and are shown to recover the double-peak structure suggesting the well-known ``spin-charge'' separation. By tuning the difference in velocities for the two-band fermions, we clarify the crossover in spectral functions from the spin-charge separation to the decoupled fermions. We discuss the relevance of our results to the spin-1/2 Hubbard model under a magnetic field, which can be mapped onto two-band spinless fermions.
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.