Dimensional crossover in quasi-one-dimensional and high-$T_c$ superconductors

The one-dimensional electron gas exhibits spin-charge separation and power-law spectral responses to many experimentally relevant probes. Ordering in a quasi-one-dimensional system is necessarily associated with a dimensional crossover, at which sharp quasiparticle peaks, with small spectral weight, emerge from the incoherent background. Using methods of Abelian bosonization, we derive asymptotically correct expressions for the spectral changes induced by this crossover. Comparison is made with experiments on the high-temperature superconductors, which are electronically quasi-one-dimensional on a local scale.