Related papers: On a dual representation of the Goldstone manifold

On a dual representation of the Goldstone manifold

URL: http://arxiv.org/abs/2004.05047v1
Date: Fri, 10 Apr 2020 14:20:34 GMT
Title: On a dual representation of the Goldstone manifold
Authors: Carlos A. Jim\'enez-Hoyos and Rayner R. Rodr\'iguez-Guzm\'an and Thomas M. Henderson and Gustavo E. Scuseria
Abstract summary: An intrinsic wavefunction with a broken continuous symmetry can be rotated with no energy penalty leading to an infinite set of degenerate states. We show that a dual representation of such manifold exists that is sampled by an infinite set of non-degenerate states.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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 $|\langle \Phi | \hat{P}^q | \Phi \rangle|$ becomes very small.

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