Incoherence of single particle hopping between Luttinger liquids

Abstract

We demonstrate that for general spin-charge separated Luttinger liquids there exists a critical value of the inter-Luttinger-liquid single particle hopping, ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}^{\mathit{c}}$, 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 ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ will not exhibit split Fermi surfaces. For many Luttinger liquids, no band dipsersing 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.