Quantum Matter

I will review recent results from applying the conformal bootstrap to 3D CFTs, including precise determinations of critical exponents and in the 3D Ising and O(N) vector models, new constraints on 3D Gross-Neveu models, and general bounds on correlation function coefficients of currents and stress tensors.

In this talk, we examine the behavior of the retarded Green’s function in theories with Lifshitz scaling symmetry, both through dual gravitational models and a direct field theory approach. In contrast with the case of a relativistic CFT, where the Green’s function is fixed (up to normalization) by symmetry, the generic Lifshitz Green’s function can a priori depend on an arbitrary function Nevertheless, we demonstrate that the imaginary part of the retarded Green’s function (i.e. the spectral function) of scalar operators is exponentially suppressed in a window of frequencies near zero. This behavior is universal in all Lifshitz theories without additional constraining symmetries. On the gravity side, this result is robust against higher derivative corrections, while on the field theory side we present two z>1 examples where the exponential suppression arises from summing the perturbative expansion to infinite order, as a consequence of the energy-momentum conservation.

A hydrodynamic theory of transport in quantum mechanically phase-disordered superconductors is possible when supercurrent relaxation can be treated as a slow process. We obtain general results for the frequency-dependent conductivity of such a regime. With time-reversal invariance, the conductivity is characterized by a Drude-like peak, with width given by the supercurrent relaxation rate. Using the memory matrix formalism, we obtain a formula for this width (and hence also the dc resistivity) when the supercurrent is relaxed by short range Coulomb interactions. This leads to a new -- effective field theoretic and fully quantum -- derivation of a classic result on flux flow resistance. With strong breaking of time-reversal invariance, the optical conductivity exhibits what we call a `hydrodynamic supercyclotron' resonance. We obtain the frequency and decay rate of this resonance for the case of supercurrent relaxation due to an emergent Chern-Simons gauge field. The supercurrent decay rate in this `topologically ordered superfluid vortex liquid' is determined by the conductivities of the normal component of the liquid. Our work gives a controlled framework for low temperature metallic phases arising from phase-disordered superconductivity.

I will review and compare numerous models for metallic states without quasiparticle excitations. The solvable SYK model provides a useful starting point, and also has remarkable holographic connections to the quantum gravity of black holes in AdS2. Quantum critical states of two-dimensional metals are obtained by coupling the fermions to fluctuating bosonic order parameters or gauge fields: I will discuss their physical properties and possible connections to experiments.

I will discuss recent progress in understanding the consequences of hydrodynamic electron flow on measurable transport properties of metals, focusing on metals where the electrons behave as a charge neutral relativistic plasma. In graphene, I will connect our theoretical models with experimental data and show how we can explain features of transport in graphene that are inconsistent with quasiparticle transport. I will then discuss the extension of these results to Weyl semimetals, which are modeled by a system of multiple chiral fluids. Negative magnetoresistance can occur in both electric and thermal transport; the latter is a consequence of a distinct axial-gravitational anomaly. Future transport experiments on Weyl semimetals can discover this exotic type of anomaly in the lab.

The semimetal-superconductor quantum phase transition of 2D Dirac fermions, such as found on the surface of a topological insulator, is conjectured to exhibit an emergent N=2 supersymmetry, based on a one-loop renormalization group analysis. In this talk I will present further evidence for this conjecture based on a three-loop analysis. Assuming the conjecture is true, I will present exact results for certain critical properties including the optical conductivity, shear viscosity, and entanglement entropy at zero temperature, as well as the finite-temperature optical conductivity.

We present some recent developments in the framework of holographic (Lorentz violating) massive gravity. We rigorously define the most generic isotropic setup in 3+1 dimensions and we study in detail its phenomenology. We describe the electric and the viscoelastic responses of the system and we comment on the fate of the KSS viscosity bound in absence of translational symmetry. We conclude with some discussion hints and comments for the future.

Within the context of AdS/CFT, the gravity dual of an s-wave superfluid is given by scalar QED on an asymptotically AdS spacetime. While this conclusion is vastly based on numerical arguments, I will provide an analytical proof that this is indeed the case. In particular, I will present a technique which allows to explicitely compute the low-energy effective action for the boundary theory starting from the bulk system. This will be done for an arbitrary number of dimensions and an arbitrary potential. I will recover the known dispersion relation for conformal first sound.

I will present a hydrodynamic description of matter in a charge density wave (or "smectic") phase. As in superfluids, the spontaneous breaking of a continuous symmetry -- here translations in one direction -- adds a Goldstone phase to the usual long lived hydrodynamic variables. This phase propagates as a highly anisotropic "second sound" mode at low energies, affecting properties such as transport. Phase fluctuations, due to proliferating dislocations, give a finite life-time to certain collective modes, which can be experimentally probed e.g. by measuring ultrasound attenuation. Using the memory matrix, the hydrodynamic approach predicts sound attenuation to be proportional to the shear viscosity of the normal (non-smectic) state.