Phase relaxation and pattern formation in holographic gapless charge density waves

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.

arXiv comment25 pages + appendices, 13 figures

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• U(1) quasi-hydrodynamics: Schwinger-Keldysh effective field theory and holography
• On the hydrodynamics of (2 + 1)-dimensional strongly coupled relativistic theories in an external magnetic field
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• Microscopic Mechanism of Pair-, Charge- and Spin-Density-Wave Instabilities in Interacting D-Dimensional Fermi Liquids
• Hydrodynamic modes in holographic multiple-axion model
• The commensurate state and lock-in in a holographic model
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