Implications of Relativity on Nonrelativistic Goldstone Theorems: Gapped Excitations at Finite Charge Density

Alberto Nicolis and Federico Piazza

Phys. Rev. Lett. 110, 011602 – Published 2 January 2013; Erratum Phys. Rev. Lett. 110, 039901 (2013)

Abstract

We adapt the Goldstone theorem to study spontaneous symmetry breaking in relativistic theories at finite charge density. It is customary to treat systems at finite density via nonrelativistic Hamiltonians. Here, we highlight the importance of the underlying relativistic dynamics. This leads to seemingly new results whenever the charge in question is spontaneously broken and does not commute with other broken charges. We find that that the latter interpolate gapped excitations. In contrast, all existing versions of the Goldstone theorem predict the existence of gapless modes. We derive exact nonperturbative expressions for their gaps, in terms of the chemical potential and of the symmetry algebra.

Received 16 April 2012
Corrected 7 January 2013

DOI:https://doi.org/10.1103/PhysRevLett.110.011602

Corrections

7 January 2013

Erratum

Publisher’s Note: Implications of Relativity on Nonrelativistic Goldstone Theorems: Gapped Excitations at Finite Charge Density [Phys. Rev. Lett. 110, 011602 (2013)]

Alberto Nicolis and Federico Piazza

Phys. Rev. Lett. 110, 039901 (2013)

Authors & Affiliations

Alberto Nicolis¹ and Federico Piazza²

¹Physics Department and Institute for Strings, Cosmology, and Astroparticle Physics, Columbia University, New York, New York 10027, USA
²Paris Center for Cosmological Physics and Laboratoire APC, 10, rue Alice Domon et Léonie Duquet, 75205 Paris, France