发表机构
University of Regina; Isfahan University of Technology（雷吉纳大学; 伊斯法罕理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于局部行列式缺陷的有限温度检验，用于判定低能谱子空间的稳定性，并给出半有限冯诺依曼代数中的谱展平原理及精确两投影公式，同时证明了行列式不等式及其单调性。
AI 中文摘要
我们给出了低能谱子空间稳定性的有限温度检验。该检验使用两个吉布斯态的α-z雷尼核的局部行列式缺陷，并限制其低能投影之间的迹L2距离。主要工具是半有限冯诺依曼代数中有界正单射算子的谱展平原理，它将局部乘积缺陷简化为精确的两投影公式。热学结果适用于具有迹类吉布斯算子的下有界附属哈密顿量，且不要求哈密顿量在算子范数意义下接近。我们给出了具有无界哈密顿量的无穷维例子。对于矩阵，该结果给出主角余项之和；对于量子比特，缺陷和热隙精确决定基态重叠。同一估计为有效低能模型中的有界可观测量提供均匀误差界。我们还证明了行列式不等式、其等式情形以及矩阵、有限和半有限情形下的z-单调性。
英文摘要
We give a finite-temperature test for the stability of low-energy spectral subspaces. The test uses a local determinant defect for the alpha-z Renyi kernel of two Gibbs states and bounds the tracial L2 distance between their low-energy projections. The main tool is a spectral-flattening principle for bounded positive injective operators in a semifinite von Neumann algebra. It reduces the local product defect to an exact two-projection formula. The thermal result applies to lower-bounded affiliated Hamiltonians with trace-class Gibbs operators and does not require the Hamiltonians to be close in operator norm. We give an infinite-level example with unbounded Hamiltonians. For matrices, the result gives a sum of principal-angle remainders. For qubits, the defect and the thermal gaps determine the ground-state overlap exactly. The same estimate gives a uniform error bound for bounded observables in an effective low-energy model. We also prove the determinant inequalities, their equality cases, and z-monotonicity in matrix, finite, and semifinite settings.
Comments56 Pages
