The U=\ensuremath{\infty} Hubbard model on a hypercubic lattice with exactly one hole is studied. It is seen that a degeneracy can occur in the maximal-spin sector. It is proved variationally that the Nagaoka (maximal spin) state is not a ground state, if degeneracy exists. We give an explicit construction of a variational state, an incommensurate spin-wave state, with energy lower than that of the Nagaoka state. For the case of more than one hole, a few examples are discussed where a degeneracy exists. \textcopyright{} 1996 The American Physical Society.The U=\ensuremath{\infty} Hubbard model on a hypercubic lattice with exactly one hole is studied. It is seen that a degeneracy can occur in the maximal-spin sector. It is proved variationally that the Nagaoka (maximal spin) state is not a ground state, if degeneracy exists. We give an explicit construction of a variational state, an incommensurate spin-wave state, with energy lower than that of the Nagaoka state. For the case of more than one hole, a few examples are discussed where a degeneracy exists. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9607126Physical review. B, Condensed matterOct 1, 19960 citations

Hole spectrum in the two-dimensional Hubbard model

C. E. I. Carneiro, Mário J. de Oliveira, Silvio R. A. Salinas +1 more

Physica C SuperconductivityMar 1, 19904 citations

Two-hole dynamics in spin ladders

Christoph Jurecka, Wolfram Brenig

We present an analytic theory for the energy spectrum of a two-leg spin ladder doped with two holes. Starting from a pseudo-fermion-bond-boson representation of the corresponding $t_{1,2}-J_{1,2}$ Hamiltonian we apply a diagrammatic approach adapted to the limit of strong rung coupling, which includes both, the coupling of holes to the spin background as well as the two-hole interactions. The two-hole spectrum is calculated and the formation of bound states is discussed. Additionally the evolution of the spin gap of the ladder upon doping is analyzed. A comparison with existing exact diagonalization data is presented and good agreement is found.We present an analytic theory for the energy spectrum of a two-leg spin ladder doped with two holes. Starting from a pseudo-fermion-bond-boson representation of the corresponding $t_{1,2}-J_{1,2}$ Hamiltonian we apply a diagrammatic approach adapted to the limit of strong rung coupling, which includes both, the coupling of holes to the spin background as well as the two-hole interactions. The two-hole spectrum is calculated and the formation of bound states is discussed. Additionally the evolution of the spin gap of the ladder upon doping is analyzed. A comparison with existing exact diagonalization data is presented and good agreement is found.

arXiv:cond-mat/0107365Jul 17, 20010 citations

Spin gap in coupled quarter-filled Hubbard ladders

Bernhard Edegger, Hans Gerd Evertz, R. M. Noack

Bulletin of the American Physical SocietyMar 22, 20050 citations

Instability of the Haldane phase: Roles of charge fluctuations and Hund's coupling

Satoshi Nishimoto

We systematically investigate the stability of the symmetry-protected topological (SPT) Haldane phase in spin- 1 2 Heisenberg and half-filled Hubbard ladders coupled by ferromagnetic Hund's interactions. Using the density-matrix renormalization group method, we analyze key signatures of the Haldane phase: long-range string order, finite spin gap, and characteristic entanglement spectrum degeneracies. In spin-only Heisenberg ladders, we find immediate onset and continuous strengthening of the Haldane phase with increasing Hund's coupling. In contrast, the inclusion of charge fluctuations in Hubbard ladders leads to a nontrivial stability regime, revealing a robust yet bounded region where SPT order persists despite significant charge fluctuations. We identify distinct boundaries separating a trivial insulating phase from the Haldane SPT phase, governed by both Coulomb repulsion and Hund's coupling. Our results highlight the subtle interplay of spin and charge degrees of freedom in correlated itinerant systems and establish essential criteria for observing Haldane physics experimentally in fermionic ladder materials.We systematically investigate the stability of the symmetry-protected topological (SPT) Haldane phase in spin- 1 2 Heisenberg and half-filled Hubbard ladders coupled by ferromagnetic Hund's interactions. Using the density-matrix renormalization group method, we analyze key signatures of the Haldane phase: long-range string order, finite spin gap, and characteristic entanglement spectrum degeneracies. In spin-only Heisenberg ladders, we find immediate onset and continuous strengthening of the Haldane phase with increasing Hund's coupling. In contrast, the inclusion of charge fluctuations in Hubbard ladders leads to a nontrivial stability regime, revealing a robust yet bounded region where SPT order persists despite significant charge fluctuations. We identify distinct boundaries separating a trivial insulating phase from the Haldane SPT phase, governed by both Coulomb repulsion and Hund's coupling. Our results highlight the subtle interplay of spin and charge degrees of freedom in correlated itinerant systems and establish essential criteria for observing Haldane physics experimentally in fermionic ladder materials.

arXiv:2507.05089Physical review. B./Physical review. BSep 19, 20251 citation

We present an analytic theory for the energy spectrum of a two-leg spin ladder doped with two holes. Starting from a pseudo-fermion-bond-boson representation of the corresponding

t_{1,2}-J_{1,2}

Hamiltonian we apply a diagrammatic approach adapted to the limit of strong rung coupling, which includes both, the coupling of holes to the spin background as well as the two-hole interactions. The two-hole spectrum is calculated and the formation of bound states is discussed. Additionally the evolution of the spin gap of the ladder upon doping is analyzed. A comparison with existing exact diagonalization data is presented and good agreement is found.