Normal metallic states of interacting electrons: Luttinger liquid versus Fermi liquid

C. Di Castro, Claudio Castellani, Walter Metzner

Walter Metzner, C. Di Castro

The low-energy properties of interacting Fermi systems are highly constrained by conservation laws. They generally simplify the structure of the underlying renormalization group by reducing the number of independent renormalization constants. In one dimension, all properties of normal metallic fixed points are uniquely determined by separate charge and spin conservation for states near the left and right Fermi points, respectively. We construct the general Luttinger-liquid theory of one-dimensional (1D) metals directly from these conservation laws. Luttinger-liquid parameters emerge naturally from the velocities associated with the conserved currents at the Luttinger-liquid fixed point. Instead of bosonization, one may thus use techniques familiar from Fermi-liquid theory, i.e., Feynman diagrams, equations of motion, and Ward identities. The choice of a technique comprising both Fermi- and Luttinger-liquid theory makes the similarities and differences of both theories particularly transparent, and sets the stage for constructing non-Fermi-liquid metallic fixed points in d>1. Several generic properties and asymptotic conservation laws of 2D non-Fermi-liquid metals are discussed.

Claudio Castellani, C. Di Castro

Johannes Voit, Theoretische Physik, Universität Bayreuth +1 more

Abstract. I give a brief introduction to Luttinger liquids. Luttinger liquids are paramagnetic one-dimensional metals without Landau quasi-particle excitations. The elementary excitations are collective charge and spin modes, leading to charge-spin separation. Correlation functions exhibit power-law behavior. All physical properties can be calculated, e.g. by bosonization, and depend on three parameters only: the renormalized coupling constant Kρ, and the charge and spin velocities. I also discuss the stability of Luttinger liquids with respect to temperature, interchain coupling, lattice effects and phonons, and list important open problems. WHAT IS A LUTTINGER LIQUID ANYWAY? Ordinary, three-dimensional metals are described by Fermi liquid theory. Fermi liquid theory is about the importance of electron-electron interactions in metals. It states that there is a 1:1-correspondence between the low-energy excitations of a free Fermi gas, and those of an interacting electron liquid which are termed “quasiparticles” [1]. Roughly speaking, the combination of the Pauli principle with low excitation energy (e.g. T ≪ EF) and the large phase space available in 3D, produces

Heinz J. Schulz, Gianaurelio Cuniberti, P. Pieri

Ya-Hui Zhang, Zheng Zhu

Inspired by the recent discovery of superconductivity in the nickelate ${\mathrm{Nd}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Ni}{\mathrm{O}}_{2}$, we study a generalized $t\text{\ensuremath{-}}J$ model to investigate the correlated phases induced by doping spin-1 ${\mathrm{Ni}}^{2+}$ into a spin-$1/2$ Mott insulator formed by ${\mathrm{Ni}}^{1+}$. Based on a three-fermion parton mean-field analysis, we identify a robust fractional Fermi liquid (FL*) phase for almost every doping level. The FL* state is characterized by a small Fermi pocket on top of a spin liquid, which violates the Luttinger theorem of a conventional Fermi liquid and is an example of a symmetric pseudogap metal. Furthermore, we verify our theory in one dimension through density matrix renormalization group simulations on both the generalized $t\text{\ensuremath{-}}J$ model and a two-orbital Hubbard model. The fractional Fermi liquid reduces to a fractional Luttinger liquid (LL*) in one dimension, which is connected to the conventional Luttinger liquid through a continuous quantum phase transition by tuning interaction strength. Our findings offer insights into correlated electron phenomena in nickelate superconductors and other multiorbital transition-metal oxides with a spin-triplet ${d}^{8}$ state.