Dimensional Crossovers in the Doped Ladder System: Spin Gap, Superconductivity and Interladder Coherent Band Motion

TL;DR

This study uses the perturbative renormalization group approach to analyze how weak interladder coupling affects the phase transitions and dimensional crossovers in doped Hubbard ladder systems, revealing conditions for spin gap and superconductivity.

Contribution

It provides a detailed phase diagram for doped Hubbard ladders showing the dominance of two-particle crossover and superconductivity over one-particle crossover due to intraladder interactions.

Findings

Suppression of one-particle crossover by intraladder interactions.

Existence of a region where d-wave superconductivity occurs.

Comparison of crossovers in ladder systems versus weakly coupled chains.

Abstract

Based on the perturbative renormalization group (PRG) approach, we have studied dimensional crossovers in Hubbard ladders coupled via weak interladder one-particle hopping, $t_{\perp}$. We found that the one-particle crossover is strongly suppressed through growth of the intraladder scattering processes which lead the isolated Hubbard ladder system toward the spin gap metal (SGM) phase. Consequently when $t_{\perp}$ sets in, there exists, for any finite intraladder Hubbard repulsion, $U>0$, the region where the two-particle crossover dominates the one-particle crossover and consequently the d-wave superconducting transition, which is regarded as a bipolaron condensation, occurs. By solving the scaling equations for the interladder one-particle and two-particle hopping amplitudes, we give phase diagrams of the system with respect to $U$, $t_{\perp0}$ (initial value of $t_{\perp}$) and the temperature, $T$. We compared the above dimensional crossovers with those in a weakly coupled chain system, clarifying the difference between them.