Ferromagnetic transition and phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping
Ferromagnetic transition and phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping
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DOI：
10.1103/physrevb.58.2635
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发表时间：
1997-12
影响因子：
3.7
通讯作者：
S. Daul;R. Noack
中科院分区：
文献类型：
--
作者：
S. Daul;R. Noack
利用精确对角化、密度矩阵重整化群、Edwards变分分析以及对双链Hubbard模型弱耦合计算的自适应，研究了下近邻跳变的一维Hubbard模型的相图。我们发现强耦合相图的大部分区域是铁磁的，并且在一个铁磁相中连接了三个物理上不同的极限情况。在相图中有两个弱耦合费米点的一点上，我们仔细研究了从顺磁状态到完全极化状态的相变作为现场库仑排斥的函数。我们给出了二阶跃迁的证据，并用数值方法确定了临界指数。在此参数范围内，系统可以被描述为弱耦合的Luttinger液体。我们提取了Luttinger-liquid参数，并展示了它们的行为与近邻Hubbard模型的不同之处。一般的弱耦合相图可以映射到双链哈伯德模型相图上。我们明确地展示了适应相图，并通过使用密度矩阵重整化群数值计算自旋和电荷间隙来确定其有效性。
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.