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.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.

arXiv:2505.05350Physical review. B./Physical review. BMay 29, 20250 citations

Doping dependence of the spectral function in the t−J model

R. Eder, Y. Ohta

Physica C SuperconductivityMay 1, 19961 citation

Ground-state properties of the two-dimensional antiferromagnetic Heisenberg model

Mark Gross, Eduardo Sánchez-Velasco, Eric D. Siggia

The ground-state energy, staggered magnetization, and correlation function are computed for the two-dimensional spin-(1/2 quantum antiferromagnetic Heisenberg model (believed to be relevant to the high-temperature superconducting materials without doping) on lattices up to 24\ifmmode\times\else\texttimes\fi{}24 by Monte Carlo methods extrapolated to zero temperature. A more accurate value for the ground-state energy is determined by the method of Neumann and Ulam by extrapolating from lattices up to 12\ifmmode\times\else\texttimes\fi{}12.The ground-state energy, staggered magnetization, and correlation function are computed for the two-dimensional spin-(1/2 quantum antiferromagnetic Heisenberg model (believed to be relevant to the high-temperature superconducting materials without doping) on lattices up to 24\ifmmode\times\else\texttimes\fi{}24 by Monte Carlo methods extrapolated to zero temperature. A more accurate value for the ground-state energy is determined by the method of Neumann and Ulam by extrapolating from lattices up to 12\ifmmode\times\else\texttimes\fi{}12.

Physical review. B, Condensed matterFeb 1, 1989113 citations

Two-dimensional t-J model at moderate doping

A. Sherman, M. Schreiber

arXiv:cond-mat/0302356The European Physical Journal BMar 1, 200341 citations

Renormalization of elementary excitations of the 2D t-J model at moderate doping

A. Sherman

Physics Letters AJan 1, 19952 citations

Charge carrier correlation in the electron-doped t−J model

P. W. Leung

We study the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}{t}^{\ensuremath{''}}\text{\ensuremath{-}}J$ model with parameters chosen to model an electron-doped high-temperature superconductor. The model with one, two, and four charge carriers is solved on a 32-site lattice using exact diagonalization. Our results demonstrate that at doping levels up to $x=0.125$ the model possesses robust antiferromagnetic correlation. When doped with one charge carrier, the ground state has momenta $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0)$ and $(0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi})$. On further doping, charge carriers are unbound and the momentum distribution function can be constructed from that of the single-carrier ground state. The Fermi surface resembles that of small pockets at single-charge-carrier ground-state momenta, which is the expected result in a lightly doped antiferromagnet. This feature persists upon doping up to the largest doping level we achieved. We therefore do not observe the Fermi surface changing shape at doping levels up to 0.125.We study the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}{t}^{\ensuremath{''}}\text{\ensuremath{-}}J$ model with parameters chosen to model an electron-doped high-temperature superconductor. The model with one, two, and four charge carriers is solved on a 32-site lattice using exact diagonalization. Our results demonstrate that at doping levels up to $x=0.125$ the model possesses robust antiferromagnetic correlation. When doped with one charge carrier, the ground state has momenta $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0)$ and $(0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi})$. On further doping, charge carriers are unbound and the momentum distribution function can be constructed from that of the single-carrier ground state. The Fermi surface resembles that of small pockets at single-charge-carrier ground-state momenta, which is the expected result in a lightly doped antiferromagnet. This feature persists upon doping up to the largest doping level we achieved. We therefore do not observe the Fermi surface changing shape at doping levels up to 0.125.

arXiv:cond-mat/0508035Physical Review BFeb 2, 20064 citations

x=0.125

the model possesses robust antiferromagnetic correlation. When doped with one charge carrier, the ground state has momenta $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0)$ and $(0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi})$. On further doping, charge carriers are unbound and the momentum distribution function can be constructed from that of the single-carrier ground state. The Fermi surface resembles that of small pockets at single-charge-carrier ground-state momenta, which is the expected result in a lightly doped antiferromagnet. This feature persists upon doping up to the largest doping level we achieved. We therefore do not observe the Fermi surface changing shape at doping levels up to 0.125.