Some sum rules for the non-Fermi liquids: new applications taking into account the mass renormalization factor

TL;DR

This paper extends the analysis of non-Fermi liquid Green functions within the Hubbard model, incorporating mass renormalization effects and exploring new coupled-layer systems with potential experimental implications.

Contribution

It introduces a mass renormalization factor into sum rules for non-Fermi liquids and applies the moment approach to coupled Hubbard layers, revealing new physical features.

Findings

Mass renormalization significantly affects physical quantities.

Derived relations between non-Fermi liquid parameters and interactions.

Predicted experimental signatures in coupled Hubbard layers.

Abstract

Re-studying the non-fermi liquid one-particle Green function (NFLGF) we have extended the work of A. Balatsky (Phil. Mag. Lett. 68, 251 (1993)) and L. Yin and S. Chakravarty (Int. J. Mod. Phys. B 10, 805 (1996)), among others. We used the moment approach of W. Nolting (Z. Phys. 255, 25 (1972)) to compute the unknown parameters of the NFLGF's in the framework of the Hubbard model. The zeroth order momentum requires that our one-particle Green function describe fermionic degrees of freedom. In order to satisfy the first order sum rule a renormalization, $\gamma\neq 1$, of the free electron mass is called for. The second order sum rule or moment imposes a relation between the non-Fermi liquid parameter, $\alpha$, the Coulomb interaction, U, and the frequency cutoff, $\omega_c$. We have calculated the effect of the mass renormalization factor, $\gamma$, on some physical quantities. As a new class of non-Fermi liquid systems, in Appendix A, we have studied two inequivalent coupled Hubbard layers for which we calculated the one-particle spectral functions on the layers and perpendicular to them. We discuss the new features which appear due to the shift in the two effective chemical potentials and proposed some experiments to detect the features founded from our expressions.