论文标题
在戈德斯通歧管的双重代表中
On a dual representation of the Goldstone manifold
论文作者
论文摘要
可以旋转具有断裂的连续对称性的固有波函数，而无需惩罚，导致一组无限的堕落状态被称为金石歧管。在这项工作中，我们表明存在这种歧管的双重表示，该歧管由一组无限的非分类状态采样。提供了两个表示等效的证明。从Peierls和Yoccoz（Proc。Phys。Soc。A{\ BF 70}，381（1957））的工作中，众所周知，使用发电机坐标试验波函数从Goldstone歧管获得具有良好对称性的集体状态。我们表明，类似的发生器坐标可以在双表示中使用。我们使用固有波函数提供数值证据，其中包含粒子数对称性的BE ATOM的电子结构，而H $ _5 $ ring则提供了$ \ hat {s}^z $对称性破坏。我们讨论如何使用双重表示在标准$ | \langleφ|时评估对称性态的期望值。 \ hat {p}^q | φ\ rangle | $变得很小。
An intrinsic wavefunction with a broken continuous symmetry can be rotated with no energy penalty leading to an infinite set of degenerate states known as a Goldstone manifold. In this work, we show that a dual representation of such manifold exists that is sampled by an infinite set of non-degenerate states. A proof that both representations are equivalent is provided. From the work of Peierls and Yoccoz (Proc. Phys. Soc. A {\bf 70}, 381 (1957)), it is known that collective states with good symmetries can be obtained from the Goldstone manifold using a generator coordinate trial wavefunction. We show that an analogous generator coordinate can be used in the dual representation; we provide numerical evidence using an intrinsic wavefunction with particle number symmetry-breaking for the electronic structure of the Be atom and one with $\hat{S}^z$ symmetry-breaking for a H$_5$ ring. We discuss how the dual representation can be used to evaluate expectation values of symmetry-projected states when the norm $|\langle Φ| \hat{P}^q | Φ\rangle|$ becomes very small.
