Sliding Luttinger liquid with alternating interwire couplings

We study a phase diagram for the sliding Luttinger liquid (SLL) of coupled one-dimensional quantum wires packed in a two-dimensional array in the absence of a magnetic field. We analyse whether the nearest-neighbour inter-wire interactions, stabilise the SLL phase. We construct an analogue of a Su-Schriefer-Heeger (SSH) model (allowing alternating couplings between wires). Calculating the scaling dimensions of the two most relevant perturbations, charge-density wave, and superconducting inter-wire couplings, but excluding the inter-wire single-particle hybridisation, we find a finite stability region for the SLL. It emerges due to the inter-wire forward scattering interaction, and remains stable up to a significant asymmetry between alternating couplings.