有限跳跃下二维Majorana-Hubbard模型的费米子袋研究
Fermion bag study of the two-dimensional Majorana-Hubbard model at finite hopping
- Wake Forest University（维克森林大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究通过哈密顿量费米子袋量子蒙特卡洛方法，首次在有限跳跃下模拟二维Majorana-Hubbard模型，消除符号问题并验证了半金属相及相互作用增强U(1)二聚化的理论预测。
AI中文摘要：
在$\pi$-通量晶格上的二维Majorana-Hubbard模型涉及每个位点有一个相对论性Majorana费米子的晶格上最局域的相互作用。该模型被预测具有Majorana半金属、二聚化相以及具有涌现$U(1)$对称性的量子临界点。该模型的非微扰晶格计算仍然是一个主要的开放挑战，迄今仅限于零跳跃。我们使用基于哈密顿量费米子袋的量子蒙特卡洛模拟，在有限跳跃下研究该模型。该方法基于连续时间展开，其玻尔兹曼权重是维度由展开阶数决定的矩阵的Pfaffian，并给出权重的符号。符号问题的严重性与自由跳跃矩阵中零模的位置相关，对于耦合$g\lesssim 0.7$和$\beta=L/4$，在至少$256$个位点的晶格上，符号问题被完全消除。相互作用强度$g>0$增强了$U(1)$带电的二聚化双重态，并抑制了中性通道，正如重正化群所预测的那样。增加相互作用还恢复了二聚化关联函数中在键取向交换下为偶的分量中的$U(1)$对称性，但奇分量则不然。在具有晶格向列对称性的奇分量中持续存在各向异性。数据与在整个符号问题最小窗口内无间隙半金属一致。
英文摘要：
The two-dimensional Majorana-Hubbard model on the $π$-flux lattice involves the most local interaction possible for a lattice with one relativistic Majorana fermion per site. It is predicted to host a Majorana semimetal, dimerized phases, and quantum-critical points with an emergent $U(1)$ symmetry. Nonperturbative lattice calculations for this model remain a major open challenge, thus far limited to zero hopping. We present quantum Monte Carlo simulations of the model at finite hopping using Hamiltonian fermion bags, which are based on a continuous-time expansion with Boltzmann weights that are Pfaffians of a matrix with dimension set by the expansion order, and which give the sign of the weight. Sign problem severity is related to the location of zero modes in the free hopping matrix, and for couplings $g\lesssim 0.7$ and $β=L/4$ it is fully removed for lattices up to at least $256$ sites. The interaction strength $g>0$ enhances the $U(1)$-charged dimerization doublet and suppresses the neutral channel, as the renormalization group predicts. Increasing the interactions also restores $U(1)$ symmetry in the component of the dimerization correlator that is even under bond orientation exchange, but not its odd component. There is a persistent anisotropy in the odd component with the symmetry of a lattice nematic. The data is consistent with a gapless semimetal throughout the sign-problem-minimal window.
