I will describe recent work illustrating general relations between the transport properties and chaotic properties of quantum field theories with holographic duals. I will firstly show how a simple analysis of near-horizon dynamics yields exact constraints on the spectrum of collective excitations. I will then describe how this can be exploited to identify a universal feature in the spectrum, and its implications for the collective transport properties of strongly interacting field theories with gravity duals.

Superfluids are one of the hallmarks of 20th century physics. Superfluid phases of matter are typically described at low energies and nonzero temperatures by an effective theory, the Landau-Tisza two-fluid model, which assumes the co-existence of a superfluid, dissipationless flow and a normal, dissipative flow. At zero temperature, the flow becomes entirely superfluid. In this case, a (relativistic) quantum effective action for the Goldstone has been written, and further works have studied finite temperature corrections. Holographic superfluids have also been shown to be described by the Landau-Tisza model, for the most part. I will then move on to explain how holographic superfluids with a Lifshitz-invariant quantum critical IR geometry lead to a non-vanishing normal component at zero temperature, suggesting that these are not described by the universal relativistic quantum effective action mentioned above. I will also explain how this could be relevant for recent measurements of the superfluid density and ac conductivity at low temperatures in overdoped high Tc superconductors.

Generalised global symmetries or higher-form symmetries are a novel concept in quantum field theories that enables the formulation of a conservation of higher-dimensional objects. While standard (zero-form) symmetries act on local operators, a one-form symmetry can act on the one-dimensional Wilson line. These symmetries can be discrete, continuous, broken, anomalous, etc. In Nature, the simplest realisation of a continuous one-form symmetry stems from the conservation of the number of magnetic flux lines due to the absence of magnetic monopoles. The fact that such symmetries must play a crucial role in the formulation of effective field theories has led to the first, and so far best understood application: the theory of magnetohydrodynamics, which is the theory of long-range excitations in magnetised plasmas. In this review talk, I will first discuss the mathematical details of generalised global symmetries. I will then focus on the new theory of magnetohydrodynamics and summarise how it interpolates between previously known theories (standard non-relativistic magnetohydrodynamics, force-free electrodynamics, dynamics of fermions in the lowest Landau level) and enables to find their systematic corrections. The presentation of other applications of generalised global symmetries will include generic string liquids, superfluids and the theory of elasticity. Finally, I will show how generalised global symmetries can be implemented in AdS/CFT and discuss how the construction of the holographic dual to a plasma with dynamical magnetic fields gives rise to a strongly coupled field theory with dynamical photons and extends magnetohydrodynamics into the ultraviolet regime.

Effective theories are very useful to extract transport properties at
long wavelengths, which can be done by studying the response to
external sources and geometric deformations. In two dimensions one can
also take advantage of particle-vortex duality which allows a similar
description for Quantum Hall states and superfluids/superconductors
using statistical gauge fields. I will discuss the effective theory
description of two-dimensional states with broken parity and
time-reversal invariance and the relation between odd transport and
symmetry and topological properties of the state.

It was conjectured over 50 years ago that electrons in a high quality conductor could flow collectively as a viscous fluid, just like air or water.  While impurities and umklapp scattering forbid this behavior in conventional metals, it has now become possible to study electrons that flow like classical fluids in high quality devices.  I will overview the nature of hydrodynamic transport in electrons together with some recent experiments that allow us to directly probe this behavior.

Because the cuprate superconductors are doped Mott insulators, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. We consider the Hatsugai-Kohmoto model, an exactly solvable system that is a prototypical Mott insulator above a critical interaction strength at half filling. Upon doping or reducing the interaction strength, our exact calculations show that the system becomes a non-Fermi liquid metal with a superconducting instability. In the presence of a weak pairing interaction, the instability produces a thermal transition to a superconducting phase, which is distinct from the BCS state, as evidenced by a gap-to-transition temperature ratio exceeding the universal BCS limit. The elementary excitations of this superconductor are not Bogoliubov quasiparticles but rather superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state.

An unexpected feature of this model is that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies as seen in the cuprates.

In this talk, I will review a recent reformulation of fluid dynamics as an effective field theory based on an underlying Schwinger-Keldysh path integral. Based solely on the microscopic symmetries, such as CPT invariance and unitarity, I will show how additional constraints on transport arise. As a non-trivial check of the formalism, I will show how to derive the Schwinger-Keldyh effective actions for hydrodynamics from holography.

Glasses (amorphous solids) are known to universally exhibit anomalous properties at low temperatures very different from their crystalline counterparts. Specifically, below 1-2 K the specific heat C_p (T) of glasses shows a linear temperature dependence and the thermal conductivity k(T) a quadratic dependence on temperature -in contrast with the expected cubic behavior of crystals following Debye’s theory-, that has been ascribed to the ubiquitous existence of tunneling two-level systems (TLS). Moreover, at a few K, k (T) of glasses exhibits a plateau and the specific heat a broad peak in C_p/T ³, which has been associated to an excess in the Debye-reduced vibrational density of states g(w)/w ² (the “boson peak”). In the last decades, some disordered crystals such as orientational glasses (a.k.a. “glassy crystals”), obtained by quenching a plastic crystal phase, have been found to present the very same glassy features. Nevertheless, recent works are casting doubts about this universality of “glassy behavior”. On the one hand, some genuine amorphous solids have been found to lack TLS at low temperatures, whereas some truly crystalline solids, devoid of orientational disorder, seem to exhibit those glassy features.

 

I will discuss this fascinating topic by presenting our recent experiments on different molecular solids, ranging from crystals with a minimal amount of disorder exhibiting glassy behavior to the special case of “ultrastable glasses”, aiming to shed light on this issue.

Hydrodynamics assumes local equilibration and equilibration assumes ergodic mixing driven by chaos --- at least in semi-classical systems. For a generic such system the timescales of macroscopic thermalization and onset of microscopic chaos are very different. Nevertheless, it is a pillar of Boltzmann transport that long-time equilibration can be computed from microscopic dynamics. We show how in these systems the two timescales are in fact related. Moreover, we show that a similar connection between both scales surprisingly also exists in extremely strongly coupled systems through a phenomenon christened pole-skipping in hydrodynamic response.

Understanding most basic thermodynamic properties of the liquid state such as energy and heat capacity turned out to be a long-standing problem in physics [1]. Landau&Lifshitz textbook states that no general formulas can be derived for liquid thermodynamic functions because the interactions are both strong and system-specific. Phrased differently, liquids have no small parameter. Recent experimental and theoretical results open a new way to understand liquid thermodynamics on the basis of collective modes (phonons) as is done in the solid state theory. There are important differences between phonons in solids and  liquids, and we have recently started to understand and quantify this difference. I will review collective modes in liquids including high-frequency solid-like transverse modes and will discuss how a gap in the reciprocal space emerges and develops in their spectrum [2]. This reduces the number of phonons with temperature,  consistent with the experimental decrease of constant-volume specific heat with temperature [1].  I will discuss the implication of the above theory for fundamental understanding of liquids. I will also mention how this picture can be extended above the critical point where the recently proposed Frenkel line on the phase diagram separates liquid-like and gas-like states of supercritical dynamics [1,3-5].

I will subsequently describe our recent work where we calculated the minimal quantum viscosity in terms of fundamental physical constants and compared this minimum to the bound of Kovtun, Son&Strarinets [6]. Finally, I will note the similarity of the kinematic viscosity of liquids and the quark-gluon plasma.

1. K. Trachenko and V. V. Brazhkin, Collective modes and thermodynamics of the liquid state, Reports on Progress in Physics 79, 016502 (2016).
2. C. Yang, M. T. Dove, V. V. Brazhkin and K. Trachenko, Physical Review Letters 118, 215502 (2017).
3. V. V. Brazhkin and K. Trachenko, Physics Today 65(11), 68 (2012).
4. V. V. Brazhkin et al, Physical Review Letters 111, 145901 (2013).
5. D. Bolmatov, V. V. Brazhkin and K. Trachenko, Nature Comm. 4:2331 (2013).
6. K. Trachenko and V Brazhkin, Minimal quantum viscosity from fundamental physical constants, Science Adv. arXiv:1912.06711

Dealing with nature, being on the right track may have the effect

that out of the blue surprises starts raining down in the laboratory.

AdS/CMT may be in such a state. How ARPES disqualified the cuprate

quantum critical point proving the presence of holography style

strange metal phases. How graphene style nano-transport devices

appear to pick up hydrodynamical electron flow in such a strange

metal, seemingly implying the governance of the minimal viscosity.

How transport properties in the cuprate spin stripes in very large

magnetic fields reveal the fingerprints of the “second” quantum

critical sector. When time- and co-authors permit, how the same

stuff lingers on in the overdoped regime co-existing with an

unreasonable Fermi-liquid.