AI 中文总结
研究在一维自旋哈伯德模型中探寻量子莫特半金属相，通过特定投影和引入自旋耦合构建模型，利用ED和DMRG方法研究，发现该相有自旋狄拉克费米子与中性自旋模式共存，打破对称性会使莫特半金属转变为绝缘体，为莫特半金属基态提供证据并揭示与TBG物理的关联。
AI 中文摘要
拓扑能带中的莫特物理最近备受关注，尤其是在扭曲双层石墨烯（TBG）背景下，但稳定该物理的关键因素仍不明晰。本文展示了一种量子莫特半金属相作为一维自旋哈伯德模型的基态，其每个晶胞仅一个轨道，受空间反演和粒子-空穴对称性保护。从双轨道模型出发，通过特定投影得到新晶格模型。仅哈伯德U时基态为铁磁，引入反铁磁自旋耦合J可稳定电荷中心c = 3的莫特半金属相。利用精确对角化（ED）和密度矩阵重整化群（DMRG）方法表明该相有自旋狄拉克费米子与中性自旋模式共存。打破粒子-空穴对称性会使莫特半金属转变为莫特绝缘体，二者通过连续相变分离，极化跃变为1/2。本工作首次为莫特半金属基态提供了无偏证据，表明该一维模型虽无万尼尔阻碍却捕捉到了TBG物理的一些关键方面。
英文摘要
Mott physics in topological bands has recently attracted considerable attention, particularly in the context of twisted bilayer graphene (TBG). However, the essential ingredients for stabilizing this physics remain unclear. Here, we demonstrate a quantum Mott semimetal phase as the ground state within a one-dimensional spinful Hubbard model featuring only one orbital per unit cell, protected by inversion and particle-hole symmetries. We start from a two-orbital model where a localized $f$ orbital on the A sublattice hybridizes with a delocalized $c$ orbital on the B sublattice. Projecting the $f$-orbital Hubbard $U$ onto the active flat band yields a lattice model with Wannier orbitals centered on the B sublattice. Similar to TBG, a momentum-space scale $k_*$ emerges, setting the interaction range in the projected model to $1/k_*$. While the ground state is ferromagnetic with only the Hubbard $U$, introducing an inter-site antiferromagnetic spin coupling $J$ stabilizes a Mott semimetal$^*$ phase with a central charge $c=3$. Using exact diagonalization (ED) and density matrix renormalization group (DMRG) methods, we show that this phase hosts a spinful Dirac fermion coexisting with a neutral spin mode -- analogous to the fractionalized Fermi liquid (FL$^*$) phase in higher dimensions. Furthermore, breaking particle-hole (PH) symmetry via dispersion transforms the Mott semimetal into a Mott insulator, which is separated from a distinct Mott insulating phase by a continuous transition with a polarization jump of $1/2$. Our work provides the first unbiased evidence of a Mott semimetal ground state and demonstrates that this 1D model captures some essential aspects of TBG physics, despite lacking a Wannier obstruction.
