Soft Phonon Theorems

TL;DR

This paper derives new soft theorems for gapless modes in condensed matter systems, linking scattering behavior to broken spacetime symmetries, and identifies special classes of theories with enhanced soft limits.

Contribution

It introduces novel soft theorems for Nambu-Goldstone bosons in solids, fluids, and framids, connecting scattering constraints to broken spacetime symmetries and classifying exceptional theories.

Findings

Derived soft theorems for gapless modes in various condensed matter systems.

Linked soft theorems to specific broken symmetries like translations and boosts.

Identified subclasses of theories with enhanced soft behavior through bootstrap methods.

Abstract

A variety of condensed matter systems describe gapless modes that can be interpreted as Nambu-Goldstone bosons of spontaneously broken Poincar\'e symmetry. In this paper we derive new soft theorems constraining the tree-level scattering of these degrees of freedom, as exhibited in solids, fluids, superfluids, and framids. These soft theorems are in one-to-one correspondence with various broken symmetries, including spacetime translations, Lorentz boosts, and, for the case of fluids, volume-preserving diffeomorphisms. We also implement a bootstrap in which the enhanced vanishing of amplitudes in the soft limit is taken as an input, thus sculpting out a subclass of exceptional solid, fluid, and framid theories.