On the "effective exponent theory" of the Coulomb Luttinger liquid
Yasha Gindikin, V. A. Sablikov
TL;DR
This paper critiques the 'effective exponent theory' for Coulomb Luttinger liquids, highlighting its inaccuracies in calculating dynamic correlators due to improper handling of long-range Coulomb interactions.
Contribution
The paper identifies fundamental flaws in the effective exponent theory, especially its treatment of long-range Coulomb potential and the determination of the scaling cutoff.
Findings
Effective exponent theory fails for Coulomb Luttinger liquids.
Incorrect calculation of dynamic correlators due to long-range potential handling.
Lacks a consistent method for the scaling cutoff in Coulomb interactions.
Abstract
The "effective exponent theory", developed by Wang, Millis and Das Sarma in [Phys. Rev. B 69, 167101 (2004), Phys. Rev. B 64, 193307 (2001)], fails to calculate correctly the dynamic correlators of Coulomb Luttinger liquid. Main drawbacks are (i) cutting off the Coulomb potential by killing its long-range component, (ii) the absence of non-contradictory procedure to determine the 'scaling cutoff' and correlation functions for true Coulomb interaction.
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Taxonomy
TopicsMaterial Science and Thermodynamics · Spectral Theory in Mathematical Physics · Differential Equations and Boundary Problems