Phase transitions in the Haldane-Hubbard model
Phase transitions in the Haldane-Hubbard model
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DOI：
10.1103/physrevb.109.035126
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发表时间：
2023-11
影响因子：
3.7
通讯作者：
Wan-Xiu He;Rubem Mondaini;Hong-Gang Luo;Xiaoqun Wang;Shijie Hu
中科院分区：
文献类型：
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作者：
Wan-Xiu He;Rubem Mondaini;Hong-Gang Luo;Xiaoqun Wang;Shijie Hu
Haldane-Hubbard 模型是能带拓扑和电子相互作用综合效应的一个典型例子。我们重新审视其半填充时的旋转相图，因为目前缺乏对 SU($2$) 对称性存在的共识。首先，我们利用 Hartree-Fock 平均场方法，该方法突破了可以获得自旋依赖性的有效质量项，提供了对对称性的直接理解。我们的结果与之前的研究一致，为陈数 $C=1$ 的状态提供了指导性的见解，只有一个自旋物种保持拓扑状态。除此之外，我们通过大规模无限密度矩阵重正化群（iDMRG）方法对 Haldane-Hubbard 模型的相图进行了数值研究。相边界由陈数和从传递矩阵谱获得的相关长度确定。与之前的研究不同，iDMRG 方法研究了薄且无限长的圆柱体上的 Haldane-Hubbard 模型，并检查了与二维热力学极限一致的场景。在这里，我们获得的相图定性超出了 Hartree-Fock 范围，特别是在 $C=1$ 区域，并作为进一步理论和实验研究的定量基准。
The Haldane-Hubbard model is a prime example of the combined effects of band topology and electronic interaction. We revisit its spinful phase diagram at half-filling as a consensus on the presence of SU($2$) symmetry is currently lacking. To start, we utilize the Hartree-Fock mean-field method, which offers a direct understanding of symmetry breaking through the effective mass term that can acquire spin dependence. Our results, in agreement with previous studies, provide an instructive insight into the regime where the Chern number $C=1$, with only one spin species remaining topological. Besides that, we numerically study the phase diagram of the Haldane-Hubbard model via a large-scale infinite-density matrix renormalization group (iDMRG) method. The phase boundaries are determined by the Chern number and the correlation lengths obtained from the transfer-matrix spectrum. Unlike previous studies, the iDMRG method investigates the Haldane-Hubbard model on a thin and infinitely long cylinder and examines scenarios consistent with the two-dimensional thermodynamic limit. Here, the phase diagram we obtained qualitatively goes beyond the Hartree-Fock scope, particularly in the $C=1$ region, and serves as a quantitative benchmark for further theoretical and experimental investigations.