行列式量子蒙特卡洛中抗符号问题的奇异值探测方法
Sign-problem-resilient singular-value probe in determinant quantum Monte Carlo
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中文总结 AI 辅助
该研究提出利用时空费米子矩阵低能奇异值的相邻间隙比，作为行列式量子蒙特卡洛中抗符号问题的探测工具，成功追踪到两类哈伯德模型中相互作用驱动的相变。
中文摘要 AI 辅助
符号问题限制了行列式量子蒙特卡洛对强关联费米子系统的研究。在自旋通道哈伯德-斯特拉托诺维奇解耦中，自旋关联与辅助场关联精确相关，这表明反铁磁相变会重组辅助场构型，进而改变所得费米子矩阵的统计结构。我们利用时空费米子矩阵低能奇异值的相邻间隙比，探测两个半填充蜂窝晶格哈伯德模型中相互作用驱动的相变：在无符号蜂窝哈伯德模型中，该统计量追踪到从狄拉克半金属到反铁磁莫特绝缘体的已确立相变；在复权重霍尔丹-哈伯德模型中，该相变敏感特征在相淬灭参考系综中仍可见，且接近先前估计的相变点。此外，尽管平均相位迅速被抑制，但在所研究的区域内，相位重加权仅微弱改变间隙比。这些结果确立了奇异值统计量作为行列式量子蒙特卡洛中抗符号问题的、用于探测相互作用驱动相变的工具。
英文摘要
The sign problem limits determinant quantum Monte Carlo studies of strongly correlated fermion systems. In the spin-channel Hubbard-Stratonovich decoupling, spin correlations are exactly related to auxiliary-field correlations. This relation implies that an antiferromagnetic transition reorganizes auxiliary-field configurations and thereby changes the statistical structure of the resulting fermion matrices. We use the adjacent gap ratio of low-lying singular values of the space-time fermion matrix to probe interaction-driven transitions in two half-filled honeycomb-lattice Hubbard models. In the sign-free honeycomb Hubbard model, the statistic tracks the established transition from a Dirac semimetal to an antiferromagnetic Mott insulator. In the complex-weight Haldane-Hubbard model, the transition-sensitive feature remains visible in the phase-quenched reference ensemble and occurs near previous estimates of the transition. Moreover, phase reweighting only weakly modifies the gap ratio over the regimes investigated, despite the rapid suppression of the average phase. These results establish singular-value statistics as a sign-problem-resilient probe of interaction-driven transitions in determinant quantum Monte Carlo.
