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RENORMALIZATION CONSTANT FOR A ONE-DIMENSIONAL ELECTRON-GAS

Yr Jang, Byung Il Min

Published Jan 1, 1993• 0 citations
OpenAlex

Abstract

The renormalization constant for a one-dimensional (1D) interacting electron gas is investigated within the framework of the GW approximation. It is found that the renormalization constant for the 1D interacting electron gas becomes zero in contrast to the case of a non-interacting electron gas, which implies that the Coulomb interaction makes the 1D electron gas system an unconventional Fermi liquid. Results for the 1D system are discussed in comparison with the known properties for the 2D and 3D electron gases.

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The renormalization constant for a one-dimensional (1D) interacting electron gas is investigated within the framework of the GW approximation. It is found that the renormalization constant for the 1D interacting electron gas becomes zero in contrast to the case of a non-interacting electron gas, which implies that the Coulomb interaction makes the 1D electron gas system an unconventional Fermi liquid. Results for the 1D system are discussed in comparison with the known properties for the 2D and 3D electron gases.
We review some of our recent results on the potential scattering in a weakly interacting one-dimensional(1D) electron gas. The technique we developed is a poor man's renormalization group procedure in the scattered wave basis. This technique can treat the renormalizations of the scattering on the barrier and the scattering between the electrons in a coherent way, and it allows us to find the scattering amplitudes on a localized potential of arbitrary strength for electrons at any energy. The obtained phase shifts are used to study the Fermi-edge singularity in an interacting 1D electron system, where anomalous exponent of the power-law singularity in the vicinity of the edge is found. The transmission coefficient is directly related to the conductance of a 1D channel by the Landauer formula. Simple formulas that describe the conductance at any temperature are derived. In spin-[Formula: see text] systems, the electron–electron backscattering induces renormalizations of the interaction constants, which causes the low-temperature conductance to deviate from the results of the Luttinger liquid theory. In particular, the temperature dependence of the conductance may become nonmonotonic. In the presence of a magnetic field, backscattering gives rise to a peak in the differential conductance at bias equal to the Zeeman splitting.
Renormalization group methods are used to study the low-energy behavior of the unscreened Coulomb interaction in a one-dimensional electron system. By applying a GW approximation, a strong wavefunction renormalization is found in the model, as well as renormalization of the Fermi velocity. This may have significant effects depending on the filling level of the system. The effective couplings remain bounded at arbitrarily low energies so that, in spite of the long-range character of the interaction, the system still falls into the Luttinger liquid universality class.
We study the unscreened Coulomb interaction in a one-dimensional electron system at low-energy. We use renormalization group methods and a GW approximation, in order to analyze the model. This yields both a strong wavefunction renormalization and a renormalization of the Fermi velocity. The significance of the effects depends on the filling level of the Fermi system. Despite the long-range character of the interaction, the system still falls into the Luttinger liquid universality class, since the effective couplings remain bounded at arbitrarily low energies.
The unique property of Coulomb interaction in strict one-dimensional (1D) system is revealed that the Coulomb repulsion energy of paired electrons is divergent. As consequences, electrons in 1D system can not doubly occupy the same spatial orbital and are completely localized. Numerical simulation by time dependent Hartree-Fock approximation shows this distinct property. The '0.7 anomaly' in 1D electron gas is fully explained by the property. Its possible contribution to strongly correlated systems is discussed.
Abstract The 1D interacting electron gas is very different from its higher dimensional counterparts. The main difference being the breakdown of Fermi liquid theory in 1D. In Chapter 15 we saw that the main achievement of the Fermi liquid theory is that it enables us to picture the elementary excitations in terms of quasi particles. As we shall see in this chapter, the quasi particle excitations are in 1D electron systems replaced by the Luttinger–Tomonaga excitations, a sort of density waves, having a completely different nature. The corresponding electron liquid is denoted the Luttinger liquid.