Condensed Matter

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.

In 2014 Hartnoll proposed that the diffusion constants of incoherent metals should be bounded as $ D \geq \hbar v^2/ (k_B T)$, where v is a characteristic velocity. In this talk I will describe a large class of holographic theories that saturate such a bound, with $v$ being the velocity of the butterfly effect. Our results suggest a novel connection between transport at strong coupling and the field of quantum chaos.

Non-relativistic geometries that violate hyperscaling have been used as holographic laboratories for probing strongly coupled phases with anomalous scalings. In this talk I will discuss holographic computations of DC conductivities in gravitational systems that exhibit such scalings, and allow for momentum dissipation. I will also comment on the cases in which one obtains a linear temperature dependence for the resistivity.

Ultracold atomic Fermi gases near Feshbach resonances or in optical lattices realize paradigmatic, strongly interacting forms of fermionic matter. Topological excitations and spin-charge correlations can be directly imaged in real time. In resonant fermionic superfluids, we observe the cascade of solitonic excitations following a pi phase imprint. A planar soliton decays, via the snake instability, into vortex rings and long-lived solitonic vortices. For fermions in optical lattices, realizing the Fermi-Hubbard model, we detect charge and antiferromagnetic spin correlations with single-site resolution. At low fillings, the Pauli and correlation hole is directly revealed. In the Mott insulating state, we observe strong doublon-hole correlations, which should play an important role for transport.

Quantum many-body systems are challenging to study because of their exponentially large Hilbert spaces, but at the same time they are an area for exciting new physics due to the effects of interactions between particles. For theoretical purposes, it is convenient to know if such systems can be expressed in a simpler way in terms of some nearly-free quasiparticles, or more generally if one can construct a large set of operators that approximately commute with the system’s Hamiltonian. In this talk I will discuss two ways of using the entanglement spectrum to tackle these questions. In the first part, I will show that strongly disordered systems in the many-body localized phase have a universal power-law structure in their entanglement spectra. This is a consequence of their local integrability, and distinguishes such states from typical ground states of gapped systems. In the second part, I will introduce a notion of “interaction distance” and show that the entanglement spectrum can be used to quantify “how far” an interacting ground state is from a free

(Gaussian) state. I will discuss some examples of quantum spin chains and outline a few future directions.

 

[1] M. Serbyn, A. Michailidis, D. Abanin, Z. Papic, arXiv:1605.05737.

[2] C. J. Turner, K. Meichanetzidis, Z. Papic, and J. K. Pachos, arXiv:1607.02679.