Weakly coupled one-dimensional Mott insulators

We consider a model of one-dimensional Mott insulators coupled by a weak interchain tunnelling $t_\perp$. We first determine the single-particle Green's function of a single chain by exact field-theoretical methods and then take the tunnelling into account by means of a Random Phase Approximation (RPA). In order to embed this approximation into a well-defined expansion with a small parameter, the Fourier transform $T_\perp(k)$ of the interchain coupling is assumed to have a small support in momentum space such that every integration over transverse wave vector yields a small factor $\kappa_0^2 \ll 1$. When \tp(0) exceeds a critical value, a small Fermi surface develops in the form of electron and hole pockets. We demonstrate that Luttinger's theorem holds both in the insulating and in the metallic phases. We find that the quasi-particle residue $Z$ increases very fast through the transition and quickly reaches a value of about $0.4-0.6$. The metallic state close to the transition retains many features of the one-dimensional system in the form of strong incoherent continua.Comment: 14 pages, 13 figure

Multi-orbital physics in lithium-molybdenum purple-bronze: going beyond paradigm

We investigate the role of inter-orbital fluctuations in the low energy physics of a quasi-1D material - lithium molybdenum purple bronze (LMO). It is an exceptional material that may provide us a long sought realization of a Tomonaga-Luttinger liquid (TLL) physics, but its behaviour at temperatures of the order of $T^*\approx 30$K remains puzzling despite numerous efforts. Here we make a conjecture that the physics around $T^*$ is dominated by multi-orbital excitations. Their properties can be captured using an excitonic picture. Using this relatively simple model we compute fermionic Green's function in the presence of excitons. We find that the spectral function is broadened with a Gaussian and its temperature dependence acquires an extra $T^1$ factor. Both effects are in perfect agreement with experimental findings. We also compute the resistivity for temperatures above and below critical temperature $T_o$. We explain an upturn of the resistivity at 28K and interpret the suppression of this extra component of resistivity when a magnetic field is applied along the conducting axis. Furthermore, in the framework of our model, we qualitatively discuss and consistently explain other experimentally detected peculiarities of purple bronze: the breaking of Wiedmann-Franz law and the magnetochromatic behaviour