利用保真度映射揭示量子相变的新方法
Novel Approach to Unveil Quantum Phase Transitions Using Fidelity Map
摘要：
在凝聚态模型中，保真度方法已被广泛用于探测各种类型的量子相变，包括一些超出朗道对称性破缺理论的相变。然而，在一些非常规相的模型中，如自旋1的Kitaev-Heisenberg模型中的量子自旋液体相，精确定位相变点仍然是一个挑战。在这项工作中，我们提出了一种新的方法，我们命名为保真度地图，检测量子相变具有更高的精度和灵敏度相比，传统的保真度措施。我们的计划扩展了保真度的概念，从一个单一的维度量到一个多维的数量，并使用元启发式算法搜索的关键点，全局最大化的保真度在每个阶段。我们在三个相互作用凝聚态模型中测试了该方案，即由量子自旋液体相和拓扑Haldane相组成的自旋1 Kitaev Heisenberg模型、具有Berezinskiii-Kosterlitz-Thouless跃迁的自旋1/2 XXZ模型和具有拓扑量子相变的Su-Schrieffer-Heeger模型。结果表明，保真度图可以准确地捕捉到大范围的相变，从而为研究未知模型中的相变提供了一种新的工具，而无需事先知道系统的对称性。
英文摘要：
Fidelity approach has been widely used to detect various types of quantum phase transitions, including some that are beyond the Landau symmetry breaking theory, in condensed matter models. However, challenges remain in locating the transition points with precision in several models with unconventional phases such as the quantum spin liquid phase in spin-1 Kitaev-Heisenberg model. In this work, we propose a novel approach, which we named the fidelity map, to detect quantum phase transitions with higher accuracy and sensitivity as compared to the conventional fidelity measures. Our scheme extends the fidelity concept from a single dimension quantity to a multi-dimensional quantity, and use a meta-heuristic algorithm to search for the critical points that globally maximized the fidelity within each phase. We test the scheme in three interacting condensed matter models, namely the spin-1 Kitaev Heisenberg model which consists of the quantum spin liquid phase and the topological Haldane phase, the spin-1/2 XXZ model which possesses a Berezinskii-Kosterlitz-Thouless transition, and the Su-Schrieffer-Heeger model that exhibits a topological quantum phase transition. The result shows that the fidelity map can capture a wide range of phase transitions accurately, thus providing a new tool to study phase transitions in unseen models without prior knowledge of the system's symmetry.
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