Damping of Pseudo-Goldstone Fields

TL;DR

This paper demonstrates that the damping of pseudo-Goldstone modes in various condensed matter and QCD systems can be fully characterized by their mass and diffusion coefficients within hydrodynamics, with implications for resistivity and strange metals.

Contribution

It establishes a universal hydrodynamic framework linking pseudo-Goldstone damping to their mass and diffusion, applicable across multiple physical systems.

Findings

Pseudo-Goldstone damping is determined by mass and diffusion coefficients.

Damping contributes to resistivity independently of disorder strength.

Linear temperature dependence of resistivity can arise from diffusive bounds.

Abstract

Approximate symmetries abound in Nature. If these symmetries are also spontaneously broken, the would-be Goldstone modes acquire a small mass, or inverse correlation length, and are referred to as pseudo-Goldstones. At nonzero temperature, the effects of dissipation can be captured by hydrodynamics at sufficiently long scales compared to the local equilibrium. Here we show that in the limit of weak explicit breaking, locality of hydrodynamics implies that the damping of pseudo-Goldstones is completely determined by their mass and diffusive transport coefficients. We present many applications: superfluids, QCD in the chiral limit, Wigner crystal and density wave phases in the presence of an external magnetic field or not, nematic phases and (anti-)ferromagnets. For electronic density wave phases, pseudo-Goldstone damping generates a contribution to the resistivity independent of the strength of disorder, which can have a linear temperature dependence provided the associated diffusivity saturates a bound. This is reminiscent of the phenomenology of strange metal high $T_c$ superconductors, where charge density waves are observed across the phase diagram.