Criterion for stability of Goldstone Modes and Fermi Liquid behavior in a metal with broken symmetry

Understand

There are few general physical principles that protect the low energy excitations of a quantum phase.

• Of these, Goldstone's theorem and Landau Fermi liquid theory are the most relevant to solids.
• We investigate the stability of the resulting gapless excitations - Nambu Goldstone bosons (NGBs) and Landau quasiparticles - when coupled to one another, which is of direct relevance to metals with a broken continuous symmetry.
• Typically, the coupling between NGBs and Landau quasiparticles vanishes at low energies leaving the gapless modes unaffected.