2009/06/30 by Chris R. Laumann, C. R. Laumann, S. A. Parameswaran +1 · 1 citation
Physics and Astronomy · #Advanced Condensed Matter Physics #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #cond-mat.quant-gas #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.80.144415
published as Phys. Rev. B 80, 144415 (2009) · 6 pages, 2 figures
arxiv created 2009/09/30 · openalex publication_date 2009/10/19 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04
We discuss symmetry breaking quantum phase transitions on the oft studied Bethe lattice in the context of the ferromagnetic scalar spherical model or, equivalently, the infinite Nf limit of ferromagnetic models with O(Nf) symmetry. We show that the approach to quantum criticality is characterized by the vanishing of a gap to just the global modes so that all local correlation functions continue to exhibit massive behavior. This behavior persists into the broken symmetry phase even as the order parameter develops an expectation value and thus there are no massless Goldstone bosons in the spectrum. We relate this feature to a spectral property of the graph Laplacian shared by the set of ``expander'' graphs, and argue that our results apply to symmetry breaking transitions on such graphs quite generally.