A continuous line of Berezinskii–Kosterlitz–Thouless phase transition points and the golden ratio point in the three-component fermion ladder

The realization of the three-component fermion ladder is feasible with current experimental techniques. However, due to complicated interactions among multi-components, theoretical explorations of the system are limited. In this study, we use the bosonization approach to investigate the three-component fermion ladder. We find that the interaction between the third component and the other two alters the system's kinetic structure, giving rise to a continuous line of Berezinskii-Kosterlitz-Thouless transition points in the parameter space and thereby yielding a richer structure of Berezinskii-Kosterlitz-Thouless transitions. We identify a special point, corresponding to the golden ratio under specific approximations, which marks the crossover between weak and strong interaction regimes. This study enhances understanding of the intricate dynamics governing the phase transitions in the three-component fermion ladder and paves the way for future research on one-dimensional multi-component fermion systems.