非均匀周期XY自旋1/2模型的几何相变和量子相变
Geometric phase and quantum phase transition in an inhomogeneous periodic XY spin-1/2 model
摘要：
几何相位的概念最近被引入到从几何角度分析多体系统的量子相变中。本文研究了横场中周期为2的非均匀各向异性XY模型的基态的几何相位。该模型包含了一组常见的自旋模型作为其特例，并表现出更丰富的临界行为。通过Jordan-Wigner变换映射到费米子系统上，构造相应的正则变换，实现耦合在$k$ -空间中的哈密顿量的对角化，得到了精确解.结果表明，在某些参数区域可能存在多个量子相变点，这些相变点对应于Berry曲率的发散或极值性质。
英文摘要：
The notion of geometric phase has been recently introduced to analyze the quantum phase transitions of many-body systems from the geometrical perspective. In this work, we study the geometric phase of the ground state for an inhomogeneous period-two anisotropic XY model in a transverse field. This model encompasses a group of familiar spin models as its special cases and shows a richer critical behavior. The exact solution is obtained by mapping on a fermionic system through the Jordan-Wigner transformation and constructing the relevant canonical transformation to realize the diagonalization of the Hamiltonian coupled in the $k$-space. The results show that there may exist more than one quantum phase transition point at some parameter regions and these transition points correspond to the divergence or extremum properties of the Berry curvature.
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