Cascading Multicriticality in Nonrelativistic Spontaneous Symmetry Breaking

TL;DR

This paper explores how nonrelativistic spontaneous symmetry breaking can produce higher-order Nambu-Goldstone modes with cascading criticality, evading relativistic no-go theorems through hierarchical scale phenomena.

Contribution

It introduces the concept of cascading multicriticality in nonrelativistic systems and generalizes the CHMW theorem to account for infrared divergences and scale hierarchies.

Findings

Discovery of cascading phenomena with large scale hierarchies

Evasion of relativistic CHMW theorem constraints

Protection of higher-order dispersion modes by polynomial shift symmetries

Abstract

Without Lorentz invariance, spontaneous global symmetry breaking can lead to multicritical Nambu-Goldstone modes with a higher-order low-energy dispersion $\omega\sim k^n$ ($n=2,3,\ldots$), whose naturalness is protected by polynomial shift symmetries. Here we investigate the role of infrared divergences and the nonrelativistic generalization of the Coleman-Hohenberg-Mermin-Wagner (CHMW) theorem. We find novel cascading phenomena with large hierarchies between the scales at which the value of $n$ changes, leading to an evasion of the "no-go" consequences of the relativistic CHMW theorem.