Two-band electronic metal and neighboring spin liquid (spin Bose-metal) on a zigzag strip with longer-ranged repulsion

We consider an electronic model for realizing the Spin Bose-metal (SBM) phase on a 2-leg triangular strip -- a spin liquid phase found by D.~N.~Sheng~\textit{et~al.} [Phys. Rev. B {\bf 79}, 205112 (2009)] in a spin-1/2 model with ring exchanges. Starting from a two-band ``C2S2'' metal, the SBM can be viewed as a ``C1S2'' Mott insulator with gapped overall conducting charge mode. We consider extended repulsive interactions motivated by the ab initio derivation of an electronic model for $\kappa$-ET spin liquid material [K.~Nakamura~\textit{et~al.}, J. Phys. Soc. Jpn. {\bf 78}, 083710(2009)]. Using weak coupling renormalization group analysis, we find that such interactions allow much wider C2S2 metallic phase than in the Hubbard model with on-site repulsion only. We identify a valid eight-fermion Umklapp term that is crucial for producing a Mott insulator and use Bosonization to study phases obtained out of the C2S2 metal upon increasing overall repulsion strength, finding that the SBM phase is a natural outcome for extended interactions.