CONFINEMENT AND TRANSVERSE CONDUCTIVITY IN COUPLED LUTTINGER LIQUIDS

One-particle interchain hopping in a system of coupled Luttinger Liqui ds 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 alpha wh ich characterizes the one-dimensional (1D) Luttinger liquid. Moderate intrachain interactions can lead to a strong reduction of this splitti ng. The onset of the confinement within the individual chains (defined by a vanishing splitting) seems to be governed by alpha. We give nume rical evidence that interchain coherent hopping can be totally suppres sed for alpha similar to 0.4 or even smaller alpha values. The transve rse conductivity is shown to exhibit a strong incoherent part. Even wh en coherent interchain hopping is believed to occur (at small alpha va lues), it is shown that the coherent Drude weight is always significan tly smaller than the incoherent weight. Implications for the optical e xperiments in quasi-1D organic or high-T-c superconductors are outline d.