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Journal of Physics Conference Series

Spectral functions in a two-velocities Tomonaga-Luttinger Liquid

E. Orignac, Masahisa Tsuchiizu, Yoshikazu Suzumura

Published Dec 14, 2012• 1 citation
Publisher

Abstract

We obtain the spectral functions of a two-velocities Tomonaga-Luttinger liquid at T = 0K in terms of the Appell hypergeometric functions F 1 and F 2 . In the case of SU(N) spin symmetry, the spectral functions can be expressed with the Gauss hypergeometric functions. We discuss the singularities and thresholds of the spectral functions for both the SU(N) invariant case and the general case.

DOI
10.1088/1742-6596/391/1/012163

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We obtain the spectral functions of a two-velocities Tomonaga-Luttinger liquid at T = 0K in terms of the Appell hypergeometric functions F 1 and F 2 . In the case of SU(N) spin symmetry, the spectral functions can be expressed with the Gauss hypergeometric functions. We discuss the singularities and thresholds of the spectral functions for both the SU(N) invariant case and the general case.
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.
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.
Results for the one-particle Green's function for the Tomonaga-Luttinger model of one-dimensional interacting fermions take a simple form using space and time variables. To obtain the corresponding spectral functions which determine photoemission and inverse-photoemission spectra, a double Fourier transform is necessary. For the model including spin we present analytical and numerical results. They show drastic differences from the spinless case. Expressions for the critical indices which determine the singularities of the spectra are given.
We evaluate the spectral function of interacting fermions in one dimension. Contrary to the Tomonaga-Luttinger model, our treatment accounts for the nonlinearity of the free fermion spectrum. In a striking departure from the Luttinger liquid theory, the spectrum nonlinearity restores the main feature of the Fermi liquid: a Lorentzian peak in the spectral function on the particle mass shell. At the same time, the spectral function displays a power-law singularity on the hole mass shell, similar to that in the Luttinger liquid.
We compute the spectral function rho (q, omega ) of the one-dimensional Luttinger model. We discuss the distinct influences of charge-spin separation and of the anomalous dimensions of the fermion operators and their evolution with correlation strength. Charge-spin separation shows up in finite spectral weight at frequencies between v sigma q and v rho q, where v sigma and v rho are the velocities of spin and charge fluctuations, while spectral weight above v rho q and below -v rho q is generated by the hybridization of the Fermi surface at +or-k F by interactions. There are non-universal power-law singularities at these special frequencies. We discuss the consistency of recent photoemission experiments on low-dimensional conductors with a Luttinger-liquid picture, which then would suggest very strong long-range interactions. It is pointed out that many-particle correlation functions in principle exhibit similar singularities, but they probe different and complementary aspects of the Fermi-surface interactions.