2020/04/10 by Carlos A. Jiménez-Hoyos, Jiménez-Hoyos, Carlos A., Rayner R. Rodríguez-Guzmán +5
Mathematics · #Advanced Operator Algebra Research #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2004.05047
openalex publication_date 2020/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Sz symmetry-breaking for a H5 ring. We discuss how the dual representation can be used to evaluate expectation values of symmetry-projected states when the norm |⟨ Φ| Pq | Φ⟩| becomes very small.