We study the phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping using exact diagonalization, the density-matrix renormalization group, the Edwards variational ansatz, and an adaptation of weak-coupling calculations on the two-chain Hubbard model. We find that a substantial region of the strong-coupling phase diagram is ferromagnetic, and that three physically different limiting cases are connected in one ferromagnetic phase. At a point in the phase diagram at which there are two Fermi points at weak coupling, we study carefully the phase transition from the paramagnetic state to the fully polarized one as a function of the on-site Coulomb repulsion. We present evidence that the transition is second order and determine the critical exponents numerically. In this parameter regime, the system can be described as a Luttinger liquid at weak coupling. We extract the Luttinger-liquid parameters and show how their behavior differs from that of the nearest-neighbor Hubbard model. The general weak-coupling phase diagram can be mapped onto that of the two-chain Hubbard model. We exhibit explicitly the adapted phase diagram and determine its validity by numerically calculating spin and charge gaps using the density-matrix renormalization group.We study the phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping using exact diagonalization, the density-matrix renormalization group, the Edwards variational ansatz, and an adaptation of weak-coupling calculations on the two-chain Hubbard model. We find that a substantial region of the strong-coupling phase diagram is ferromagnetic, and that three physically different limiting cases are connected in one ferromagnetic phase. At a point in the phase diagram at which there are two Fermi points at weak coupling, we study carefully the phase transition from the paramagnetic state to the fully polarized one as a function of the on-site Coulomb repulsion. We present evidence that the transition is second order and determine the critical exponents numerically. In this parameter regime, the system can be described as a Luttinger liquid at weak coupling. We extract the Luttinger-liquid parameters and show how their behavior differs from that of the nearest-neighbor Hubbard model. The general weak-coupling phase diagram can be mapped onto that of the two-chain Hubbard model. We exhibit explicitly the adapted phase diagram and determine its validity by numerically calculating spin and charge gaps using the density-matrix renormalization group.

arXiv:cond-mat/9712310Physical review. B, Condensed matterAug 1, 1998117 citations

THE PHASE DIAGRAM OF THE HUBBARD MODEL

M W Long

Series on advances in statistical mechanicsJul 1, 19910 citations

On the Phase Diagram of the Hubbard Model

J. Monecke

physica status solidi (b)Mar 1, 19767 citations

Magnetic phase diagram of a frustrated ferrimagnetic ladder: Relation to the one-dimensional boson Hubbard model

Nedko B. Ivanov, Johannes Richter

We study the magnetic phase diagram of two coupled mixed-spin $(1,\frac{1}{2})$ Heisenberg chains as a function of the frustration parameter related to diagonal exchange couplings. The analysis is performed by using spin-wave series and exact numerical diagonalization techniques. The obtained phase diagram---containing the Luttinger liquid phase, the plateau phase with a magnetization per rung $M=1∕2$ , and the fully polarized phase---is closely related to the generic $(J∕U,\ensuremath{\mu}∕U)$ phase diagram of the one-dimensional boson Hubbard model.We study the magnetic phase diagram of two coupled mixed-spin $(1,\frac{1}{2})$ Heisenberg chains as a function of the frustration parameter related to diagonal exchange couplings. The analysis is performed by using spin-wave series and exact numerical diagonalization techniques. The obtained phase diagram---containing the Luttinger liquid phase, the plateau phase with a magnetization per rung $M=1∕2$, and the fully polarized phase---is closely related to the generic $(J∕U,\ensuremath{\mu}∕U)$ phase diagram of the one-dimensional boson Hubbard model.

arXiv:cond-mat/0604495Physical Review BApr 19, 20063 citations

Weak-coupling Ground State Phase Diagram of the One-dimensional Extended Hubbard Model

Haiming Duan

By using the bosonization approach and renormalization group analysis,we study the ground state phase diagram of one-dimensional extended Hubbard model at half-filling in the regime where U and V are both positive but less than t, finding that the system shows three distinct ground states characterized by the spin-density-wave,the charge-density-wave and the bond-charge-density-wave,respectively.These results demonstrate that the ground state phases of the extended Hubbard model are not identical with those of the conventional Hubbard model.By using the bosonization approach and renormalization group analysis,we study the ground state phase diagram of one-dimensional extended Hubbard model at half-filling in the regime where U and V are both positive but less than t, finding that the system shows three distinct ground states characterized by the spin-density-wave,the charge-density-wave and the bond-charge-density-wave,respectively.These results demonstrate that the ground state phases of the extended Hubbard model are not identical with those of the conventional Hubbard model.

Shinjang dashösi ilmiy jurniliJan 1, 20070 citations

We study the magnetic phase diagram of two coupled mixed-spin

(1,\frac{1}{2})

Heisenberg chains as a function of the frustration parameter related to diagonal exchange couplings. The analysis is performed by using spin-wave series and exact numerical diagonalization techniques. The obtained phase diagram---containing the Luttinger liquid phase, the plateau phase with a magnetization per rung

M=1∕2

, and the fully polarized phase---is closely related to the generic $(J∕U,\ensuremath{\mu}∕U)$ phase diagram of the one-dimensional boson Hubbard model.