Damping of Pseudo-Goldstone Fields.

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.

Normal Charge Densities in Quantum Critical Superfluids.

The normal density of a translation-invariant superfluid often vanishes at zero temperature, as is observed in superfluid Helium and conventional superconductors described by BCS theory. Here we show that this need not be the case. We investigate the normal density in models of quantum critical superfluids using gauge-gravity duality. Models with an emergent infrared Lorentz symmetry lead to a vanishing normal density. On the other hand, models which break the isotropy between time and space may enjoy a nonvanishing normal density, depending on the spectrum of irrelevant deformations around the underlying quantum critical ground state. Our results may shed light on recent measurements of the superfluid density and low energy spectral weight in superconducting overdoped cuprates.

Universal Relaxation in a Holographic Metallic Density Wave Phase.

In this Letter, we uncover a universal relaxation mechanism of pinned density waves, combining gauge-gravity duality and effective field theory techniques. Upon breaking translations spontaneously, new gapless collective modes emerge, the Nambu-Goldstone bosons of broken translations. When translations are also weakly broken (e.g., by disorder or lattice effects), these phonons are pinned with a mass m and damped at a rate Ω, which we explicitly compute. This contribution to Ω is distinct from that of topological defects. We show that Ω≃Gm^{2}Ξ, where G is the shear modulus and Ξ is related to a diffusivity of the purely spontaneous state. This result follows from the smallness of the bulk and shear moduli, as would be the case in a phase with fluctuating translational order. At low temperatures, the collective modes relax quickly into the heat current, so that late time transport is dominated by the thermal diffusivity. In this regime, the resistivity in our model is linear in temperature and the ac conductivity displays a significant rearranging of the degrees of freedom, as spectral weight is shifted from an off-axis, pinning peak to a Drude-like peak. These results could shed light on transport properties in cuprate high T_{c} superconductors, where quantum critical behavior and translational order occur over large parts of the phase diagram and transport shows qualitatively similar features.

Slow Relaxation and Diffusion in Holographic Quantum Critical Phases.

The dissipative dynamics of strongly interacting systems are often characterized by the timescale set by the inverse temperature τ_{P}∼ℏ/(k_{B}T). We show that near a class of strongly interacting quantum critical points that arise in the infrared limit of translationally invariant holographic theories, there is a collective excitation (a quasinormal mode of the dual black hole spacetime) whose lifetime τ_{eq} is parametrically longer than τ_{P}: τ_{eq}≫T^{-1}. The lifetime is enhanced due to its dependence on a dangerously irrelevant coupling that breaks the particle-hole symmetry and the invariance under Lorentz boosts of the quantum critical point. The thermal diffusivity (in units of the butterfly velocity) is anomalously large near the quantum critical point and is governed by τ_{eq} rather than τ_{P}. We conjecture that there exists a long-lived, propagating collective mode with velocity v_{s}, and in this case the relation D=v_{s}^{2}τ_{eq} holds exactly in the limit Tτ_{eq}≫1. While scale invariance is broken, a generalized scaling theory still holds provided that the dependence of observables on the dangerously irrelevant coupling is incorporated. Our work further underlines the connection between dangerously irrelevant deformations and slow equilibration.

dc Resistivity of Quantum Critical, Charge Density Wave States from Gauge-Gravity Duality.

In contrast to metals with weak disorder, the resistivity of weakly pinned charge density waves (CDWs) is not controlled by irrelevant processes relaxing momentum. Instead, the leading contribution is governed by incoherent, diffusive processes which do not drag momentum and can be evaluated in the clean limit. We compute analytically the dc resistivity for a family of holographic charge density wave quantum critical phases and discuss its temperature scaling. Depending on the critical exponents, the ground state can be conducting or insulating. We connect our results to dc electrical transport in underdoped cuprate high T_{c} superconductors. We conclude by speculating on the possible relevance of unstable, semilocally critical CDW states to the strange metallic region.