In this talk, I will present recent work aimed at tackling two cornerstone problems in the field of strongly correlated electrons---(1) conducting non-Fermi liquid electronic fluids and (2) the continuous Mott metal-insulator transition---via controlled numerical and analytical studies of concrete electronic models in quasi-one-dimension.  The former is motivated strongly by the enigmatic "strange metal" central to the cuprates, while the latter is pertinent to, e.g., the spin-liquid candidate 2D triangular lattice organic materials \kappa-(BEDT-TTF)_{2}Cu_{2}(CN)_{3} and EtMe_{3}Sb[Pd(dmit)_{2}]_{2}.  In the first part of the talk, I will focus on point (1) and discuss our realization on the two-leg ladder of a novel non-Fermi liquid quantum phase---the "d-wave metal"---which we construct by placing the charge sector of the electronic system into a "Bose metal" with strong d-wave correlations.  Importantly, this phase is non-perturbative in that it cannot be accessed starting from free electrons and slowly turning on interactions.  Remarkably, we are able to realize this strange metal as the ground state of reasonable microscopic Hamiltonian by augmenting the t-J model with a simple, local four-site ring-exchange interaction.  In the second half of the talk, I will discuss recent work on various half-filled electronic models on the two-leg triangular strip in which we have identified a continuous Mott transition between a metal and "spin Bose metal", where the latter is a novel Mott-insulating spin-liquid phase obtained from the former by gapping out only the overall charge mode at strong coupling.  Our Mott transition is shown to be in the XY universality class and thus constitutes a clear and direct quasi-1D analog of the elegant higher-dimensional scenario recently proposed by Senthil [1].  Finally, I will touch on the potential relevance of these studies to the actual 2D materials which inspired them:  the cuprates and the organics.

[1]  T. Senthil, PRB 78, 045109 (2008).