一维手性系统有限温度下的量子几何边界
Quantum geometric bounds at finite temperature for one-dimensional chiral systems
AI总结：
本文针对有限温度下一维手性对称系统，在混合态Uhlmann框架下建立了严格几何下界，经SSH模型和Kitaev链验证，还探讨了用量子虚时演化方法探测密度矩阵几何的途径。
AI中文摘要：
零温下，量子态的几何与拓扑通过精确边界紧密关联，该边界从下方约束几何量受拓扑不变量限制。然而有限温度下，类似关系仍不明确。本文在混合态的Uhlmann框架内，建立了有限温度下一维（1D）手性对称系统的严格几何下界，证明Bures长度受连续几何相位角约束，进一步推导了温度依赖的边界，其在零温极限与平凡高温区间插值。利用Su-Schrieffer-Heeger（SSH）模型和无自旋Kitaev链模型对结果进行了解析与数值验证，最后探讨了通过量子虚时演化（QITE）方法在量子电路中探测密度矩阵几何的潜在途径。
英文摘要：
The geometry and topology of quantum states are intimately related at zero temperature through exact bounds that constrain geometric quantities from below by topological invariants. At finite-temperature, however, the analogous relations remain unclear. Here we establish rigorous geometric lower bounds for one-dimensional (1D) chiral-symmetric systems at finite temperature within the Uhlmann's framework for mixed states. We show that the Bures length is bounded by a continuous geometric phase angle. We further derive a temperature-dependent bound that interpolates between the zero-temperature limit and a trivial high-temperature regime. Our results are verified analytically and numerically using the Su-Schrieffer-Heeger (SSH) model and the spinless Kitaev chain model. Finally, we discuss potential ways to detect the geometry of the density matrix in quantum circuits, with the quantum imaginary time evolution (QITE) method.
