Phase relaxation and pattern formation in holographic gapless charge density waves

TL;DR

This paper investigates the dynamics of spontaneous translation symmetry breaking in holographic models, revealing a gapless, algebraic phase transition characterized by an effective time-dependent Ginzburg-Landau equation and universal low-energy behavior.

Contribution

It introduces a novel holographic framework describing gapless charge density wave dynamics with a universal phase relaxation mechanism across different symmetry-breaking patterns.

Findings

The phase transition is characterized by a continuous phase relaxation rate.

The low-energy dynamics are universal and insensitive to the specific symmetry-breaking pattern.

The effective dynamics are well described by a time-dependent Ginzburg-Landau equation.

Abstract

We study the dynamics of spontaneous translation symmetry breaking in holographic models in presence of weak explicit sources. We show that, unlike conventional gapped quantum charge density wave systems, this dynamics is well characterized by the effective time dependent Ginzburg-Landau equation, both above and below the critical temperature, which leads to a "gapless" algebraic pattern of metal-insulator phase transition. In this framework we elucidate the nature of the damped Goldstone mode (the phason), which has earlier been identified in the effective hydrodynamic theory of pinned charge density wave and observed in holographic homogeneous lattice models. We follow the motion of the quasinormal modes across the dynamical phase transition in models with either periodic inhomogeneous or helical homogeneous spatial structures, showing that the phase relaxation rate is continuous at the critical temperature. Moreover, we find that the qualitative low-energy dynamics of the broken phase is universal, insensitive to the precise pattern of translation symmetry breaking, and therefore applies to homogeneous models as well.