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arXiv:cond-mat/0107633 · Physical Review Letters

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

Silke Biermann, Antoine Georges, Alexander I. Lichtenstein, Thierry Giamarchi

Published Dec 13, 2001• 107 citations
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Abstract

We investigate a system of one-dimensional Hubbard chains of interacting fermions coupled by interchain 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 interchain optical conductivity are calculated. Possible applications to organic conductors are discussed.

DOI
10.1103/physrevlett.87.276405

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•Jan 1, 2006•0 citations
We investigate a system of one-dimensional Hubbard chains of interacting fermions coupled by interchain 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 interchain optical conductivity are calculated. Possible applications to organic conductors are discussed.
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We study a half-filled ladder of spinless fermions. We show that contrary to a single chain, the ladder becomes a Mott insulator for arbitrarily small repulsive interactions. We obtain the full phase diagram and physical quantities such as the charge gap. We show that there is only a single insulating phase for repulsive interactions, regardless of the strength of the interchain hopping and single chain Mott gap. There is thus no confinement-deconfinement transition in this system but a simple crossover. Using bosonization with the renormalization group we show that upon doping the system becomes a Luttinger liquid with a universal parameter K=1/2K=1/2K=1/2 different from the one of the single chain (K=1/4).(K=1/4).(K=1/4).
We study the problem of the crossover from one- to higher-dimensional metals by considering an array of Luttinger liquids (one-dimensional chains) coupled by a weak interchain hopping ${t}_{\ensuremath{\perp}}.$ We evaluate the exact asymptotic low-energy behavior of the self-energy in the anisotropic infinite-dimension limit. This limit extends the dynamical mean-field concept to the case of a chain embedded in a self-consistent medium. The system flows to a Fermi-liquid fixed point for energies below the dimensional crossover temperature, and the anomalous exponent \ensuremath{\alpha} renormalizes to zero, in the case of equal spin and charge velocities. In particular, the single-particle spectral function shows sharp quasiparticle peaks with nonvanishing weight along the whole Fermi surface, in contrast to the lowest-order result. Our result is obtained by carrying out a resummation of all diagrams of the expansion in ${t}_{\ensuremath{\perp}}$ contributing to the anisotropic $\stackrel{\ensuremath{\rightarrow}}{D}\ensuremath{\infty}$ limit. This is done by solving, in an almost completely analytic way, an asymptotically exact recursive equation for the renormalized vertices, within a skeleton expansion. Our outcome shows that perturbation expansions in ${t}_{\ensuremath{\perp}}$ restricted to lowest orders are unreliable below the crossover temperature. The extension to finite dimensions is discussed. This work extends our recent letter [Phys. Rev. Lett. 83, 128 (1999)], and includes all mathematical details.
One-particle interchain hopping in a system of coupled Luttinger liquids is investigated using exact diagonalizations techniques. First, the two-chain problem of spinless fermions is studied in order to see the behavior of the band splitting as a function of the exponent $\ensuremath{\alpha}$ which characterizes the one-dimensional (1D) Luttinger liquid. Moderate intrachain interactions can lead to a strong reduction of this splitting. The onset of the confinement within the individual chains (defined by a vanishing splitting) seems to be governed by $\ensuremath{\alpha}$. We give numerical evidence that interchain coherent hopping can be totally suppressed for $\ensuremath{\alpha}\ensuremath{\sim}0.4$ or even smaller $\ensuremath{\alpha}$ values. The transverse conductivity is shown to exhibit a strong incoherent part. Even when coherent interchain hopping is believed to occur (at small $\ensuremath{\alpha}$ values), it is shown that the coherent Drude weight is always significantly smaller than the incoherent weight. Implications for the optical experiments in quasi-1D organic or high-Tc{T}_{c}Tc​ superconductors are outlined.
Despite the fact that by now one dimensional and three dimensional systems of interacting particles are reasonably well understood, very little is known on how to go from the one dimensional physics to the three dimensional one. This is in particular true in a quasi-one dimensional geometry where the hopping of particles between one dimensional chains or tubes can lead to a dimensional crossover between a Luttinger liquid and more conventional high dimensional states. Such a situation is relevant to many physical systems. Recently cold atoms in optical traps have provided a unique and controllable system in which to investigate this physics. We thus analyze a system made of coupled one dimensional tubes of interacting fermions. We explore the observable consequences, such as the phase diagram for isolated tubes, and the possibility to realize unusual superfluid phases in coupled tubes systems