基于换位子级数展开的混合态保真度磁化率
Mixed-state fidelity susceptibility through iterated commutator series expansion
摘要：
提出了一种微扰方法来计算热态的混合态保真度磁化率。所使用的数学技术提供了一个解析表达式的MFS作为一个正式的扩展的热力学平均值的连续更高的哈密顿算子涉及通过控制参数。该表达式自然分为两个部分：通常的等温磁化率和一个组成部分的形式的一个无限系列的热力学平均值编码的非交换性的问题。如果哈密顿量的对称性是用某个（有限维）代数的生成元给出的，则所得到的展开式可以用一个封闭的形式来计算。这个问题在几个流行的模型上进行了测试，结果表明，如果它们是基于海森堡或SU（1，1）李代数的表示理论的性质，计算要简单得多。
英文摘要：
We present a perturbative approach to the problem of computation of mixed-state fidelity susceptibility (MFS) for thermal states. The mathematical techniques used provides an analytical expression for the MFS as a formal expansion in terms of the thermodynamic mean values of successively higher commutators of the Hamiltonian with the operator involved through the control parameter. That expression is naturally divided into two parts: the usual isothermal susceptibility and a constituent in the form of an infinite series of thermodynamic mean values which encodes the noncommutativity in the problem. If the symmetry properties of the Hamiltonian are given in terms of the generators of some (finite dimensional) algebra, the obtained expansion may be evaluated in a closed form. This issue is tested on several popular models, for which it is shown that the calculations are much simpler if they are based on the properties from the representation theory of the Heisenberg or SU(1, 1) Lie algebra.
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