INCOHERENCE OF SINGLE-PARTICLE HOPPING BETWEEN LUTTINGER LIQUIDS

We demonstrate that for general spin-charge separated Luttinger liquids there exists a critical value of the inter-Luttinger-liquid single particle hopping, t(perpendicular-to)c, below which there is no coherent single particle hopping between the liquids. In the absence of coherent single particle hopping, two Luttinger liquids coupled by t(perpendicular-to) will not exhibit split Fermi surfaces. For many Luttinger liquids, no band dispersing between the liquids will form, and thus the system will retain a one-dimensional Fermi surface. This will have dramatic implications for the physical properties of such a system.