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arXiv:cond-mat/0008065 · Europhysics Letters (EPL)

Spectral functions in a magnetic field as a probe of spin-charge separation in a Luttinger liquid

Silvio Rabello, Q Si

Published Dec 1, 2002• 11 citations
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Abstract

We show that the single-particle spectral functions in a magnetic field can be used to probe spin-charge separation of a Luttinger liquid. Away from the Fermi momentum, the magnetic field splits both the spinon peak and holon peak; here the spin-charge separation nature is reflected in the different magnitude of the two splittings. At the Fermi momentum, the magnetic field splits the zero-field peak into four peaks. The feasibility of experimentally studying this effect is discussed.

DOI
10.1209/epl/i2002-00300-9

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We show that the single-particle spectral functions in a magnetic field can be used to probe spin-charge separation of a Luttinger liquid. Away from the Fermi momentum, the magnetic field splits both the spinon peak and holon peak; here the spin-charge separation nature is reflected in the different magnitude of the two splittings. At the Fermi momentum, the magnetic field splits the zero-field peak into four peaks. The feasibility of experimentally studying this effect is discussed.
By exactly analyzing the spin-12\frac{1}{2}21​ Luttinger liquid (LL) and numerically solving a model of a mobile impurity electron in the LL, we obtain the one-electron spectral function $A(p,\ensuremath{\omega})$ in a one-dimensional metal in an entire range of ppp at zero temperature. For ∣p∣|p|∣p∣ near the Fermi point pF{p}_{\mathrm{F}}pF​, $A(p,\ensuremath{\omega})$ is featured by two prominent peaks of spinon and (anti)holon representing spin-charge separation, but we also find an additional cusp structure between them. For $|p|\ensuremath{\gg}{p}_{\mathrm{F}}$, this structure evolves as a main peak in $A(p,\ensuremath{\omega})$ by swallowing the antiholon mode and its dispersion relation approaches that of a free electron, implying the existence of an electron excitation in the whole region, but not quite a quasiparticle in the Fermi liquid due to ever existing power-law decay of the excitation.
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.
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.
A system of one-dimensional electrons interacting via a short-range potential described by Hubbard model is considered in the regime of strong coupling using the Bethe ansatz approach. We study its momentum distribution function at zero temperature and find one additional singularity at the 3kF3{k}_{\mathrm{F}}3kF​ point. We identify that the second singularity is of the same Luttinger liquid type as the low-energy one at kF{k}_{\mathrm{F}}kF​. By calculating the spectral function simultaneously, we show that the second Luttinger liquid at 3kF3{k}_{\mathrm{F}}3kF​ is formed by charge modes only, unlike the known one around kF{k}_{\mathrm{F}}kF​ consisting of both spin and charge modes. This result reveals the ability of the spin-charge separation effect to split the Fermi point of free electrons into two, demonstrating its robustness beyond the low-energy limit of Luttinger liquid where it was originally found.
We consider momentum resolved tunneling between a Luttinger liquid and a two dimensional electron gas as a function of transverse magnetic field. We include the effects of an anomalous exponent and Zeeman splitting on both the Luttinger liquid and the two dimensional electron gas. We show that there are six dispersing features that should be observed in magneto-tunneling, in contrast with the four features that would be seen in a non-interacting one dimensional electron gas. The strength of these features varies with the anomalous exponent, being most pronounced when γρ=0γ_ρ=0γρ​=0. We argue that this measurement provides an important experimental signature of spin-charge separation.
We consider momentum resolved tunneling between a Luttinger liquid and a two-dimensional electron gas as a function of transverse magnetic field. We include the effects of an anomalous exponent and Zeeman splitting on both the Luttinger liquid and the two-dimensional electron gas. We show that there are six dispersing features that should be observed in magneto-tunneling, in contrast with the four features that would be seen in a noninteracting one-dimensional electron gas. The strength of these features varies with the anomalous exponent, being most pronounced when ${\ensuremath{\gamma}}_{\ensuremath{\rho}}=0$. We argue that this measurement provides an important experimental signature of spin-charge separation.