核壳势约束下两粒子的钉扎效应和类QPT行为
Pinning effect and QPT-like behavior for two particles confined by a core-shell potential
摘要：
本文研究了核壳势约束下的两电子系统的基态纠缠、能量和量子数，其中核的宽度连续变化直到它最终消失。这个简单的系统表现出丰富而复杂的行为：随着核心宽度的变化，该系统的特征在于两个特殊的转变，由于不同的原因，它显示出类似于少粒子量子相变的特征。第一次出现对应于类似于二阶量子相变的东西，而第二次转变的标志是不连续性，相对于驱动参数，在一阶导数的量，如能量和纠缠。通过对该系统的研究，可以解释在S. Abdullah等人[Phys.Rev.B80，235302（2009）]。我们还比较了核壳系统与一个系统的核心以及缺席：这表明，即使非常狭窄，核心以及有相关的“钉扎”效果。有趣的是，依赖于势对称性，当基态已经被束缚到外层（壳层）阱时，波函数的钉扎可能使系统纠缠减半或加倍（相对于无核阱系统）。在这个过程中，我们讨论了系统的保真度和显示的有用性，考虑粒子密度保真度，而不是更常用的-但更难以访问-波函数保真度。特别是，我们证明了-与无节点的空间波函数的基态-粒子密度保真度为零，当且仅当波函数保真度为零。
英文摘要：
We study the ground state entanglement, energy and fidelities of a two-electron system bounded by a core-shell potential, where the core width is varied continuously until it eventually vanishes. This simple system displays a rich and complex behavior: as the core width is varied, this system is characterized by two peculiar transitions where, for different reasons, it displays characteristics similar to a few-particle quantum phase transition. The first occurrence corresponds to something akin to a second order quantum phase transition, while the second transition is marked by a discontinuity, with respect to the driving parameter, in the first derivatives of quantities like energy and entanglement. The study of this system allows to shed light on the sudden variation of entanglement and energy observed in S. Abdullah et al. [Phys. Rev. B 80, 235302 (2009)]. We also compare the core-shell system with a system where a core well is absent: this shows that, even when extremely narrow, the core well has a relevant `pinning' effect. Interestingly, depending on the potential symmetry, the pinning of the wavefunction may either halve or double the system entanglement (with respect to the no-core-well system) when the ground state is already bounded to the outer (shell) well. In the process we discuss the system fidelity and show the usefulness of considering the particle density fidelity as opposed to the more commonly used -- but much more difficult to access -- wavefunction fidelity. In particular we demonstrate that -- for ground-states with nodeless spatial wavefunctions -- the particle density fidelity is zero if and only if the wavefunction fidelity is zero.
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