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.

Breakdown of Diffusion on Chiral Edges.

We show that dirty quantum Hall systems exhibit large hydrodynamic fluctuations at their edge that lead to anomalously damped charge excitations in the Kardar-Parisi-Zhang universality class ω≃ck-iDk^{3/2}. The dissipative optical conductivity of the edge is singular at low frequencies σ(ω)∼1/ω^{1/3}. These results are direct consequences of the charge continuity relation, the chiral anomaly, and thermalization on the edge-in particular translation invariance is not assumed. Diffusion of heat similarly breaks down, with a universality class that depends on whether the bulk thermal Hall conductivity vanishes. We further establish the theory of fluctuating hydrodynamics for surface chiral metals, where charge fluctuations give logarithmic corrections to transport.

Theory of Diffusive Fluctuations.

The recently developed effective field theory of fluctuations around thermal equilibrium is used to compute late-time correlation functions of conserved densities. Specializing to systems with a single conservation law, we find that the diffusive pole is shifted in the presence of nonlinear hydrodynamic self-interactions, and that the density-density Green's function acquires a branch point halfway to the diffusive pole, at frequency ω=-(i/2)Dk^{2}. We discuss the relevance of diffusive fluctuations for strongly correlated transport in condensed matter and cold atomic systems.

Publisher's Note: Transport Signatures of the Hall Viscosity [Phys. Rev. Lett. 119, 226602 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.119.226602.

Transport Signatures of the Hall Viscosity.

Hall viscosity is a nondissipative response function describing momentum transport in two-dimensional systems with broken parity. It is quantized in the quantum Hall regime, and contains information about the topological order of the quantum Hall state. Hall viscosity can distinguish different quantum Hall states with identical Hall conductances, but different topological order. To date, an experimentally accessible signature of Hall viscosity is lacking. We exploit the fact that Hall viscosity contributes to charge transport at finite wavelengths, and can therefore be extracted from nonlocal resistance measurements in inhomogeneous charge flows. We explain how to determine the Hall viscosity from such a transport experiment. In particular, we show that the profile of the electrochemical potential close to contacts where current is injected is sensitive to the value of the Hall viscosity.

Wess-Zumino terms for relativistic fluids, superfluids, solids, and supersolids.

We use the coset construction of low-energy effective actions to systematically derive Wess-Zumino (WZ) terms for fluid and isotropic solid systems in two, three, and four spacetime dimensions. We recover the known WZ term for fluids in two dimensions as well as the very recently found WZ term for fluids in three dimensions. We find two new WZ terms for supersolids that have not previously appeared in the literature. In addition, by relaxing certain assumptions about the symmetry group of fluids we find a number of new WZ terms for fluids with and without charge, in all dimensions. We find no WZ terms for solids and superfluids.