有限系统中的对称性破缺与量子关联：量子点、超冷玻色气体及相关核与化学方法的研究
Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods
AI总结：
本文综述小型有限系统对称性破缺研究，聚焦量子点电子与超冷玻色原子强关联区，提出结合无约束Hartree-Fock破缺与后投影恢复的两步统一描述法，经精确对角化验证，并列举四类相关强关联现象。
摘要：
本文综述了小型有限尺寸系统中出现的对称性破缺现象的研究，重点关注二维半导体量子点中电子以及简谐势阱中囚禁的超冷玻色原子的强关联区域。在整个综述过程中，我们强调了在这些系统中，以及在核物理和量子化学等以粒子间作用力差异极大为特征的更传统领域中发现的对称性破缺的普适方面与相似性。通过发展一种两步法——即在无约束Hartree-Fock（哈特里-福克）水平上进行对称性破缺，随后通过后Hartree-Fock投影技术恢复对称性——本文提出了对排斥粒子（无论是费米子还是玻色子）有限系统中强关联现象的统一描述。该两步法的定量与定性方面均通过精确对角化计算得到了处理与验证。\n由对称性破缺产生的强关联现象包括：（I）量子点分子以及在单个各向异性量子点内形成的钉扎电子分子二聚体中的化学键合、解离与纠缠（在零磁场和有限磁场下）。（II）电子结晶，粒子定域在同心多边形环的顶点上，以及在圆形量子点中形成旋转电子分子（rotating electron molecules, REMs）。（III）在强磁场下，REMs由无参数解析波函数描述，这是Laughlin（劳克林）方法和复合费米子方法的一种替代方案。（IV）强排斥玻色子的结晶相。在旋转势阱中，与REMs类似，这类排斥玻色子会形成旋转玻色子分子（rotating boson molecules, RBMs）。
英文摘要：
Investigations of emergent symmetry breaking phenomena occurring in small finite-size systems are reviewed, with a focus on the strongly correlated regime of electrons in two-dimensional semicoductor quantum dots and trapped ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize universal aspects and similarities of symmetry breaking found in these systems, as well as in more traditional fields like nuclear physics and quantum chemistry, which are characterized by very different interparticle forces. A unified description of strongly correlated phenomena in finite systems of repelling particles (whether fermions or bosons) is presented through the development of a two-step method of symmetry breaking at the unrestricted Hartree-Fock level and of subsequent symmetry restoration via post Hartree-Fock projection techniques. Quantitative and qualitative aspects of the two-step method are treated and validated by exact diagonalization calculations. Strongly-correlated phenomena emerging from symmetry breaking include: (I) Chemical bonding, dissociation, and entanglement (at zero and finite magnetic fields) in quantum dot molecules and in pinned electron molecular dimers formed within a single anisotropic quantum dot. (II) Electron crystallization, with particle localization on the vertices of concentric polygonal rings, and formation of rotating electron molecules (REMs) in circular quantum dots. (III) At high magnetic fields, the REMs are described by parameter-free analytic wave functions, which are an alternative to the Laughlin and composite-fermion approaches. (IV) Crystalline phases of strongly repelling bosons. In rotating traps and in analogy with the REMs, such repelling bosons form rotating boson molecules (RBMs).
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