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

TL;DR

This study explores the magnetic ground states of a highly doped two-leg Hubbard ladder system with a particle bath, revealing diverse magnetic phases and explaining them via an effective t-J model analysis.

Contribution

It introduces a detailed analysis of magnetic states in a doped Hubbard ladder with a particle bath, using an effective t-J model including three-site terms for the first time.

Findings

Saturated ferromagnetism appears in weak doping due to Nagaoka mechanism.

Highly doped regions exhibit partially polarized and nonmagnetic states.

The effective t-J model accurately reproduces the phase diagram and explains energy competition.

Abstract

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-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-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-J model.