论文标题
隐藏的对称性，比安奇分类和量子几何态歧管的地球学
Hidden Symmetries, the Bianchi Classification and Geodesics of the Quantum Geometric Ground-State Manifolds
论文作者
论文摘要
我们研究了依赖参数的哈密顿量的量子地面歧管的杀戮向量。我们发现，歧管的对称性可能在哈密顿量的水平上不可见，并且物质的不同量子阶段表现出不同的对称性。我们建议使用杀戮矢量场的Lie代数对基于Bianchi的各种歧管进行分类。此外，我们解释了如何利用这些对称性来找到地球学并在越过临界线时探索其行为。我们简要讨论了测量学，能量波动和绝热制备方案之间的关系。我们的主要示例是各向异性横向视野模型。我们还分析了ISIN的极限，并找到了两种情况下的测量方程的分析解决方案。
We study the Killing vectors of the quantum ground-state manifold of a parameter-dependent Hamiltonian. We find that the manifold may have symmetries that are not visible at the level of the Hamiltonian and that different quantum phases of matter exhibit different symmetries. We propose a Bianchi-based classification of the various ground-state manifolds using the Lie algebra of the Killing vector fields. Moreover, we explain how to exploit these symmetries to find geodesics and explore their behaviour when crossing critical lines. We briefly discuss the relation between geodesics, energy fluctuations and adiabatic preparation protocols. Our primary example is the anisotropic transverse-field Ising model. We also analyze the Ising limit and find analytic solutions to the geodesic equations for both cases.
