发表机构
The Institute of Mathematical Sciences; Homi Bhabha National Institute（马哈拉施特拉邦数学科学研究所; 霍米·巴巴国立研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于轮廓积分的谱投影方法，用于高效计数非厄米Wilson-Dirac算子负实轴本征值，从而可靠确定Wilson费米子行列式符号，并具有更广泛的非厄米系统应用潜力。
AI 中文摘要
大型稀疏算子的关键性质往往仅由其谱中局部化的一小部分本征模决定。在采用Wilson费米子的格点QCD中，费米子行列式的符号由非厄米Wilson-Dirac算子负实轴上本征值个数的奇偶性决定。确定这一符号具有挑战性，尤其是在近零模可能导致例外构型的参数区域。我们提出了一种基于轮廓积分的谱投影方法，用于计数非厄米Wilson-Dirac算子$D$的负实本征值，这些本征值决定了其行列式的符号。该谱投影辅以适用于移位线性系统的自适应加速收缩求解器和奇异值排除，以可靠地设定谱界和轮廓边界。我们通过系统的收敛性测试（包括轮廓尺寸的变化）证明了该方法的稳健性，并展示了其解析接近负实轴本征值的能力。除了费米子行列式符号评估外，该方法还提供了一种系统化手段，用于从密集复谱中分离出物理相关的本征值，在非厄米量子系统、稳定性分析和大规模本征值问题中具有潜在应用。
英文摘要
Key properties of a large sparse operator can often be determined by only a small, spectrally localized subset of its eigenmodes. In lattice QCD with Wilson fermions, the sign of the fermion determinant is determined by the parity of the number of eigenvalues lying on the negative real axis of the non-Hermitian Wilson-Dirac operator. Determination of this signature can be challenging, particularly in parameter regimes where near-zero modes can lead to exceptional configurations. We present a contour-integral-based spectral projection method to count the negative-real eigenvalues of the non-Hermitian Wilson-Dirac operator $D$ that determine the sign of its determinant. The spectral projection is supplemented by an adapted deflation-accelerated solver for shifted linear systems and singular-value exclusions to reliably set spectral bounds and contour boundaries. We demonstrate the robustness of the method through systematic convergence tests, including variations of the contour size, and show its ability to resolve eigenvalues close to the negative real axis. Beyond fermion determinant sign evaluation, the approach provides a systematic means of isolating physically relevant eigenvalues embedded in dense complex spectra, with potential applications to non-Hermitian quantum systems, stability analyses, and large-scale eigenvalue problems.
Comments10 pages, 2 figures, 1 Table
