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arXiv 1908.04892cond-mat.supr-conhep-thquant-ph
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超导体和超流体中的基态波函数重叠

Ground State Wave Function Overlap in Superconductors and Superfluids

Mark P. Hertzberg, Mudit Jain

摘要:

为了阐明非相对论凝聚体的量子基态结构,我们明确地构造了多种类玻色子的基态波函数,描述超导电性或超流性。由于每个场$Ψ_j$携带相位$θ_j$,并且对于独立的$α_j$,拉格朗日量在旋转$θ_j \to θ_j + α_j$下是不变的,因此可以研究因这些相位而不同的一对基态$\langle G|G'\rangle$之间的对应波函数重叠。我们在无限体积极限下操作,并通过利用位置空间核和调节UV模式,使用特定的处方来定义这些状态。我们发现,这种重叠消失的大多数对旋转,包括$θ_j \to θ_j + m_j ε$,其中$m_j$是每个物种的质量,而它是不变的变换下$θ_j \to θ_j + q_j ε$,其中$q_j$是每个物种的电荷。我们解释说,这是一致的超流体之间的区别,其中有一个非平凡的保守数,和超导体,其中的电场和保守电荷被屏蔽,而它是兼容的非零序参数在这两种情况下。此外,我们发现这种体基态波函数重叠直接反映了有效理论的Goldstone玻色子结构,并提供了一个有用的诊断其物理相。

英文摘要:

In order to elucidate the quantum ground state structure of non-relativistic condensates, we explicitly construct the ground state wave function for multiple species of bosons, describing either superconductivity or superfluidity. Since each field $Ψ_j$ carries a phase $θ_j$ and the Lagrangian is invariant under rotations $θ_j \to θ_j + α_j$ for independent $α_j$, one can investigate the corresponding wave function overlap between a pair of ground states $\langle G|G'\rangle$ differing by these phases. We operate in the infinite volume limit and use a particular prescription to define these states by utilizing the position space kernel and regulating the UV modes. We show that this overlap vanishes for most pairs of rotations, including $θ_j \to θ_j + m_j ε$, where $m_j$ is the mass of each species, while it is unchanged under the transformation $θ_j \to θ_j + q_j ε$, where $q_j$ is the charge of each species. We explain that this is consistent with the distinction between a superfluid, in which there is a non-trivial conserved number, and the superconductor, in which the electric field and conserved charge is screened, while it is compatible with a non-zero order parameter in both cases. Moreover, we find that this bulk ground state wave function overlap directly reflects the Goldstone boson structure of the effective theory and provides a useful diagnostic of its physical phase.

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