Stable 1d non-Fermi liquids and lattice theory

Patrick O’Brien

Haoyu Guo

We diagnose the stability of the Migdal-Eliashberg theory for a Fermi surface coupled to a gapless boson in 2+1 dimensions. We provide a scheme for diagonalizing the Bethe-Salpeter ladder when small-angle scattering mediated by the boson plays a dominant role. We found a large number of soft modes which correspond to shape fluctuations of the Fermi surface, and these shape deformations follow a diffusion-like dynamics on the Fermi surface. Surprisingly, the odd-parity deformations of a convex Fermi surface becomes unstable near the non-Fermi liquid regime of the Ising-Nematic quantum critical point and our finding calls for revisit of the Migdal-Eliashberg framework. The implication of the Bethe-Salpeter eigenvalues in transport will be discussed in the companion paper [H.Guo,arXiv:2311.03458].

Sudhakar Yarlagadda, Susumu Kurihara

Gergely T. Zimányi, Kevin S. Bedell

The infrared singularities of the recently introduced marginal-Fermi-liquid theory are treated within a perturbative renormalization-group approach. Marginal Fermi liquids are stable in a limited range of the parameters; otherwise non-Fermi-liquid behavior is obtained. Experimental ramifications on the conductivity and spin relaxation are discussed.

F. D. M. Haldane

The explicitly soluble Luttinger model is used as a basis for the description of the general interacting Fermi gas in one dimension, which will be called 'Luttinger liquid theory', by analogy with Fermi liquid theory. The excitation spectrum of the Luttinger model is described by density-wave, charge and current excitations; its spectral properties determine a characteristic parameter that controls the correlation function exponents. These relations are shown to survive in non-soluble generalisations of the model with a non-linear fermion dispersion. It is proposed that this low-energy structure is universal to a wide class of 1D systems with conducting or fluid properties, including spin chains.

Subhro Bhattacharjee, Sung-Sik Lee, Yong Baek Kim