DIMENSIONAL CROSSOVERS AND PHASE TRANSITIONS IN STRONGLY CORRELATED LOW-DIMENSIONAL ELECTRON SYSTEMS: RENORMALIZATION-GROUP STUDY

Abstract

Based on the perturbative renormalization-group (PRG) approach, we have examined interplay or competition between one-particle (1P) and two-particle (2P) processes in strongly correlated low-dimensional electron systems. Throughout the article, we use the Grassmann functional integral approach, since it has an advantage that the 1P degrees of freedom are incorporated in an explicit manner. We mainly discuss an array of chains weakly-coupled via interchain one-particle hopping, where the constituent chains, if isolated, have a strong-coupling fixed point, such as the Mott-insulator, spin-gap-metal, or Anderson-insulator fixed point. In such cases, quantum fluctuations evolving toward the low-energy limit strongly suppress the interchain 1P coherence, and consequently a phase transition from the incoherent metallic (ICM) phase becomes possible. This kind of competition plays a key role to elucidate the interplay of correlation and dimensionality effects in real quasi-one-dimensional (Q1D) materials in nature. As examples, we take up spin-density-wave (SDW) phase transitions in dimerized quarter-filled Hubbard chains to elucidate the nature of the magnetic phase transitions in the Q1D organic conductors, (TMTTF)2X and (TMTSF)2X. Dimensional crossover problems in Q1D Hubbard ladders are also discussed to describe the pressure-induced superconductivity in the doped ladder systems. Interplay of randomness, electron correlation, and dimensionality effects in weakly-coupled half-filled Hubbard chains with weak quenched random potentials is also studied. We also discuss some 2D electron systems where the two-loop renormalization-group procedure is well defined and works.