Crossover from Antiferromagnetic Phase to Fermiology Regime in a Weakly Coupled Half-Filled Chain System

Effects of the electron-electron umklapp process on dimensional crossovers caused by the interchain one-particle hopping, $t_{\perp}$, in a weakly-coupled half-filled chain system have been studied, based on the perturbative renormalization-group approach. The variance of $t_\perp$ and the umklapp process under scaling is taken into account. We found that the intrachain umklapp process causes a finite crossover value of $t_\perp$, $t_{\perp cr}$. For $t_{\perp}<t_{\perp c}$, as the temperature decreases, the system undergoes a crossesover from the Tomonaga-Luttinger (TL) liquid to an incipient one-dimensional Mott insulator and finally makes a phase transition into an antiferromagnetic long-range-ordered phase at a transition temperature $T_{N}$ which increases with the increasing $t_{\perp}$. For $t_{\perp}>t_{\perp c}$, the system undergoes a crossesover from the TL liquid to the Fermiology regime where the interchain propagation of a quasi-particle is coherent. We discuss relevance of the present result to the experimentally suggested, pressure-induced crossover phenomena in the quasi-one-dimensional organic systems.