An introduction to quantum liquids: Fermi liquids and collective modes

John S. Clarke

Avraham Klein, Dmitrii L. Maslov, Andrey V. Chubukov

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

Dmitri V. Khveshchenko

This Letter addresses the problem of constructing a proper bosonized description of the collective modes in strongly interacting (non-)Fermi liquids which is specific to two spatial dimensions. Although, in a mild form, this subtlety exists in the Fermi liquid as well, the discussion focuses on the effects of long-ranged and/or retarded interactions which can completely destroy the fermionic quasiparticles. The present analysis provides a further insight into the nature and properties of the collective bosonic modes in such systems.

Subhro Bhattacharjee