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arXiv · 1811.04638

Quantum Geometric Tensor in $\mathcal{PT}$-Symmetric Quantum Mechanics

Da-Jian Zhang·Qing-hai Wang·Jiangbin Gong
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Abstract

A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a Berry curvature whereas the real part induces a metric tensor on system's parameter manifold. This results in a unified conceptual framework to understand and explore physical properties of $\mathcal{PT}$-symmetric systems from a geometric perspective. To illustrate the usefulness of the extended QGT, we show how its real part, i.e., the metric tensor, can be exploited as a tool to detect quantum phase transitions as well as spontaneous $\mathcal{PT}$-symmetry breaking in $\mathcal{PT}$-symmetric systems.

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Da-Jian Zhang, Qing-hai Wang, Jiangbin Gong. 2018-11-12. Quantum Geometric Tensor in $\mathcal{PT}$-Symmetric Quantum Mechanics. https://doi.org/10.1103/physreva.99.042104

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