Deconfinement Transition and Luttinger to Fermi Liquid Crossover in Quasi-One-Dimensional Systems

Abstract

We investigate a system of one dimensional Hubbard chains of interacting fermions coupled by inter-chain hopping. Using a generalization of the Dynamical Mean Field Theory we study the deconfinement transition from a Mott insulator to a metal and the crossover between Luttinger and Fermi liquid phases. One-particle properties, local spin response and inter-chain optical conductivity are calculated. Possible applications to organic conductors are discussed.PACS numbers: 71.10. Pm,71.10.Hf,71.27+a,71.30+h The nature of the metallic phase of interacting electron systems depends strongly on dimensionality. In three dimensions, Fermi liquid (FL) theory applies, whereas in one dimension the quasi-particle concept breaks down, leading to a different kind of low-energy fixed point known as a Luttinger liquid (LL). For commensurate electron fillings, strong enough repulsive interactions destroy the metallic state altogether by opening a Mott gap. This phenomenon exists in all dimensions but the onedimensional case is particularly favorable [1]. In quasi one-dimensional (Q1D) systems, interchain hopping can induce a (deconfinement) transition from the Mott insulating (MI) state to a metallic state and crossovers between different metallic behaviors (Fig. 1). Besides their intrinsic theoretical interest, understanding these phenomena is directly relevant for a number of compounds such as the organic (super)-conductors (Bechgaard salts), which are three dimensional stacks of quarter-filled chains [2]. Indeed, in these compounds some of the low temperature properties are well described by Fermi liquid theory, whereas optical [3] and transport properties [4] have shown that the high temperature phase is either a Luttinger liquid or a Mott insulator.Describing these Q1D systems is not an easy task. The transverse hopping t ⊥ is a relevant perturbation on the LL [5,6,7]. Hence, perturbative renormalization group calculations yield an estimate of the crossover scale [5,8] but fail below that scale. In the MI state, electrons are confined on the chains by the Mott gap. A finite critical value of t ⊥ is needed to induce an insulator to metal transition. Such a transition has been advocated [9,10]to be at the root of the change from insulating to metallic behavior observed in Bechgaard salts when increasing pressure or when going from the TMTTF to the TMTSF family. Thus the effects of the inter-chain hopping that are the most important physically cannot be handled reliably by perturbative methods. Although some non- perturbative studies of deconfinement have been made for a finite number of chains [11] the case of an infinite system is still open. Some of the key questions yet to be answered are: (i) What is the crossover scale from the LL to MI, or from the LL to FL (Fig.1), and is there only one crossover scale for the different physical properties (transport, spin response, single-particle properties etc...) ? (ii) What is the nature of the low-temperature FL state, and in particular is the shape of the Fermi surface (FS) aff...

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