对称投影吉布斯态的量子化拓扑不变量
Quantized topological invariant of symmetry-projected Gibbs states
AI总结：
该研究针对三维团簇模型，利用通量扭曲膜不变量区分吉布斯态的三类相，通过量子蒙特卡罗验证了其量子化性质，为对称性保护拓扑相的研究提供了新的拓扑不变量工具。
AI中文摘要：
我们研究投影到可收缩一维形式对称性对称扇区的吉布斯态。在三维团簇模型插值中，该投影稳定了对称性保护的拓扑相和投影顺磁相，二者均与热无序相截然不同。通量扭曲膜不变量通过取值-1、+1、0区分这三个相，这些值在端点、自对偶、零温及无穷温线上是精确的；在其他区域，其量子化需要正的空间面、缠绕线和界面张力。量子蒙特卡罗通过张力诊断和直接有限尺寸估计验证了该量子化。
英文摘要：
We study Gibbs states projected onto the symmetric sector of contractible one-form symmetries. In a three-dimensional cluster-model interpolation, this projection stabilizes symmetry-protected topological and projected-paramagnetic phases, both sharply distinct from thermal disorder. A flux-twisted membrane invariant distinguishes these three phases by the values $-1,+1,0$, respectively. These values are exact on the endpoint, self-dual, zero-temperature, and infinite-temperature lines; elsewhere their quantization requires positive spatial-sheet, winding-line, and interface tensions. Quantum Monte Carlo supports the quantization through tension diagnostics and direct finite-size estimates.
