Ferromagnetic ground state of the SU(3) Hubbard model on the Lieb lattice
Ferromagnetic ground state of the SU(3) Hubbard model on the Lieb lattice
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Lieb 晶格上 SU(3) Hubbard 模型的铁磁基态
DOI：
10.1103/physreva.96.053616
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发表时间：
2016-07
影响因子：
2.9
通讯作者：
Wei Zhang
中科院分区：
文献类型：
--
作者：
Wenxing Nie;Deping Zhang;Wei Zhang
利用平均场近似方法研究了Lieb格点上从弱相互作用到强相互作用的排斥性费米SU（$3$）Hubbard模型的磁性.为了验证我们所采用的方法，我们首先讨论了SU（2 $）Hubbard模型在平均场水平，并发现我们的结果与已知的严格定理是一致的。然后，我们扩展到SU（3 $）对称的情况下的计算。我们发现，在$4/9$填充，SU$（3）$对称性自发地打破SU$（2）\次$U$（1）$对称性在基态，导致交错铁磁态的任何排斥$U$在零温度。然后，我们调查的铁磁状态的稳定性放松填充远离4/9$，并得出结论，铁磁状态是敏感的，但强大的填充物，因为它可以坚持在一定的填充制度。我们还应用有限温度下的平均场近似计算了铁磁态的临界温度和临界熵。由于每个粒子的临界熵明显大于实验中所能实现的临界熵，我们希望这种铁磁态的一些准长程有序特征可以通过将费米子碱土金属（类）原子加载到光学晶格中来实现和观察。
We investigate the magnetic properties of a repulsive fermionic SU($3$) Hubbard model on the Lieb lattice from weak to strong interaction by means of the mean-field approximation. To validate the method we employed, we first discuss the SU($2$) Hubbard model at the mean-field level, and find that our results are consistent with known rigorous theorems. We then extend the calculation to the case of SU($3$) symmetry. We find that, at $4/9$ filling, the SU$(3)$ symmetry spontaneously breaks into the SU$(2)\times$U$(1)$ symmetry in the ground state, leading to a staggered ferromagnetic state for any repulsive $U$ at zero temperature. We then investigate the stability of the ferromagnetic state by relaxing the filling away from $4/9$, and conclude that the ferromagnetic state is sensitive but robust to fillings, as it can persist within a certain filling regime. We also apply the mean-field approximation to finite temperature to calculate the critical temperature and the critical entropy of the ferromagnetic state. As the resulting critical entropy per particle is significantly greater than that can be realized in experiments, we expect some quasi-long-range-ordered features of such a ferromagnetic state can be realized and observed with fermionic alkaline-earth-metal(-like) atoms loaded into optical lattices.
DOI：
10.1201/9780429499210
发表时间：
1994
期刊：
--
影响因子：
--
作者：
H. Georgi
通讯作者：
H. Georgi