论文标题
参数依赖的弯曲空间中的量子几何张量
The Quantum Geometric Tensor in a Parameter Dependent Curved Space
论文作者
论文摘要
我们在具有参数依赖性度量的弯曲空间中引入了量子几何张量，其中包含量子度量张量作为对称部分和对应于反对称部分的浆果曲率。该参数依赖性度量可以修改通常的内部产品，从而通过添加与衍生物成正比的术语相对于度量标准的参数，从而诱导量子度量张量和浆果曲率的修改。量子度量张量以两种方式获得：通过使用参数依赖性弯曲空间中两个状态之间的无限距离的定义以及通过保真度敏感性方法。通常的浆果连接获得了一个附加的术语，弯曲的内部产品将浆果连接转换为一个对象，该对象转换为重量的连接和密度。最后，我们在一个维度上提供了三个示例，并提供了一个非平凡的度量：一个非谐波振荡器，类似摩尔斯的电势和广义的无谐振荡器；二分之一：在弯曲空间中耦合的Anharmonic振荡器。
We introduce a quantum geometric tensor in a curved space with a parameter-dependent metric, which contains the quantum metric tensor as the symmetric part and the Berry curvature corresponding to the antisymmetric part. This parameter-dependent metric modifies the usual inner product, which induces modifications in the quantum metric tensor and Berry curvature by adding terms proportional to the derivatives with respect to the parameters of the determinant of the metric. The quantum metric tensor is obtained in two ways: By using the definition of the infinitesimal distance between two states in the parameter-dependent curved space and via the fidelity susceptibility approach. The usual Berry connection acquires an additional term with which the curved inner product converts the Berry connection into an object that transforms as a connection and density of weight one. Finally, we provide three examples in one dimension with a nontrivial metric: an anharmonic oscillator, a Morse-like potential, and a generalized anharmonic oscillator; and one in two dimensions: the coupled anharmonic oscillator in a curved space.
