Quantum critical scaling of the geometric tensors.
Quantum critical scaling of the geometric tensors.
复制标题
DOI：
10.1103/physrevlett.99.095701
复制
发表时间：
2007-05
影响因子：
8.6
通讯作者：
L. Campos Venuti;P. Zanardi
中科院分区：
文献类型：
--
作者：
L. Campos Venuti;P. Zanardi
Berry相和量子信息理论的保真度概念最近被用于从几何角度分析量子相变。在这篇文章中，我们将这两种方法统一起来，表明潜在的机制是复张量在哈密顿参数空间上的临界奇异行为。这是通过在临界点附近对这个量子几何张量进行缩放分析来实现的。这样，以前的大多数结果在一般的基础上得到了理解，并发现了新的结果。我们证明了临界性并不是保证几何张量的超扩展发散的充分条件，并说明了这是可能的条件。通过对自旋1/2 XXZ海森堡链的精确对角化进一步验证了这一分析的有效性。
Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this Letter we unify these two approaches showing that the underlying mechanism is the critical singular behavior of a complex tensor over the Hamiltonian parameter space. This is achieved by performing a scaling analysis of this quantum geometric tensor in the vicinity of the critical points. In this way most of the previous results are understood on general grounds and new ones are found. We show that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible. The validity of this analysis is further checked by exact diagonalization of the spin-1/2 XXZ Heisenberg chain.