Charge-spin Separation in One-dimensional Metals and Insulators A

I discuss origin and possible experimental manifestations of charge-spin separation in 1D Luttinger and Luther-Emery liquids, the latter describing 1D Mott and Peierls insu-lators and superconductors. Emphasis is on photoemission where the spectral function generically shows two dispersing peaks associated with the collective charge and spin excitations, and on transport. I analyse the temperature dependences of the charge and spin conductivities of two organic conductors and conclude that most likely, charge-spin separation is not realized there and that they can be described as fluctuating Peierls insulators. 1 One-dimensional metals: the Luttinger liquid One of the most exciting areas in the condensed-matter many-body problem is the search for metallic non-Fermi liquid states. This has been sparked by the unusual normal-state properties of the underdoped high-T c cuprates but definite confirmation of a non-Fermi liquid state there is still pending. This is so mainly because of theoretical difficulties to establish such a picture in two dimensions and provide a unifying framework which could tie together the multitude of puzzling experimental results. The situation is precisely opposite in one dimension (1D): here the Luttinger liquid 1,2 has become a paradigm for a non-Fermi liquid metal but an unambiguous identification of a specific system as a Luttinger liquid has not been achieved yet. Unlike 2D, responsible for this is the wealth of quantitative theoretical information available to date which puts strong constraints to a Luttinger liquid interpretation of the otherwise unexplained exotic features of many experiments. Shortly, a Luttinger liquid can be described as a metal whose elementary ex-citations are not fermionic quasi-particles but collective bosonic charge and spin fluctuations. This picture emerges because the coupling of quasi-particles to collective modes is extremely strong in 1D 3. Quantitatively, one can pin down two key factors to the breakdown of the Fermi liquid and measure them by four parameters which completely describe the low-energy physics in 1D: (i) Singular Peierls-type particle-hole fluctuations which interfere with superconducting fluctuations, and which lead to non-universal power-law scaling of many properties, measured by a coupling constant K ρ : this parameter parametrizes all scaling laws between the various correlation functions. Generically, there is a similar coupling constant K σ for the spin fluctuations. However, spin-rotation invariance requires K σ = 1 and consequently , this quantity is often omitted from discussion. (ii) Charge-spin separation,