Magnetic ground states of highly doped two-leg Hubbard ladders with a particle bath

We investigate the ground-state magnetism of a Hubbard model in a system consisting of a main frame (subsystem) and a particle bath (center sites). The hole doping in the main frame is controlled by adjusting the chemical potential of the particle bath. In the weakly doped region, the saturated ferromagnetic state emerges due to the Nagaoka mechanism [Phys. Rev. B 90, 224426 (2014)]. However, in the highly doped region, a variety of intriguing magnetic states are observed, including partially polarized states and nonmagnetic states. To understand these states, we analyze the state of the subsystem by comparing its properties with those of a two-leg ladder system, which corresponds to the subsystem with the center sites removed. Furthermore, to gain insight into the microscopic origin of the magnetic phase diagram, we study the ground state of the corresponding effective $t\text{\ensuremath{-}}J$ model, derived from the Hubbard model by considering the second-order processes of the electron hopping. The phase diagram is well reproduced by the effective $t\text{\ensuremath{-}}J$ model, which includes the three-site pair-hopping term. To elucidate the competition among different energy contributions, such as potential, kinetic, and magnetic energies, we classify the energies within the effective $t\text{\ensuremath{-}}J$ model.