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Periodic Report Summary 1 - HOLOLAND (Charting the holographic quantum landscape, and consequences on charge transport at strong coupling)

1. Summary description of the project objectives

This proposal aims at elucidating the properties of charge transport at strong coupling, when no quasiparticle description is valid. We will employ techniques from gauge/gravity duality, which comes from String Theory and High Energy physics and maps a strongly-coupled field theory with a UV conformal fixed point to an asymptotically Anti-de Sitter gravitational spacetime described by Einstein’s equations. Possible applications can be found in strongly-coupled Condensed Matter systems. Scaling properties of transport at strong coupling likely originate from scaling regimes of the gravitational dual, so we will classify and chart the holographic quantum landscape following Effective Holographic Theories principles. This approach relies on specifying the symmetries and the relevant operators in the problem at hand. I expect to be able to identify such operators in phases breaking translation invariance homogeneously, build gravity models with tunable intermediate scaling regimes, characterize the phases studied with local observables (transport coefficients, correlators...) and explore connections with top-down models from String Theory. The development of hydrodynamic theories of transport when symmetries are spontaneously broken but the corresponding Goldstones are long-lived is another important direction, with applications in strongly-coupled Condensed Matter systems like graphene near the charge neutrality point (GNCP) and the high Tc superconductors (HTCs).

The main research training objectives are three-fold: complementing my set of current skills with gravitational perturbation and numerical techniques, as well as building a solid culture in modern Condensed Matter Theory. Important additional research and transferable skills are included in the training plan. At the outcome of the Fellowship, I will find myself at a privileged position at the interface between High Energy and Condensed Matter physics, able to draw research directions from both sides. I expect the proposal to be very beneficial to the ERA: it will encourage multidisciplinary exchanges, foster collaborations between France and the USA, and more generally further advances on a new and radical change of paradigm relevant for some long-standing Condensed Matter issues.

2. Description of the work performed since the beginning of the project

Since the beginning of the project, we have made progress in two interrelated directions: the description of quantum critical points which are not scale invariant but scale covariant; hydrodynamic description of transport in strongly-coupled Condensed Matter systems when the collective excitations are only approximately conserved. Beyond their intrinsic theoretical interest, these results are relevant for the physics of real Condensed Matter systems like the HTCs and GNCP, as stressed by a series of recent papers in Science reporting signatures of hydrodynamic transport in various metallic systems – so in a regime where quasiparticles are not the right description.

The first direction uses holographic quantum critical points, modelled by black holes with emergent zero temperature scaling geometries. These scaling solutions do not have to be scale invariant, which allows to construct scaling theories of thermoelectric transport which are not scale invariant but simply scale covariant. This means that the energy and charge density operators receive anomalous dimensions in the IR fixed point. We have studied how these critical exponents govern the low temperature / low frequency scalings of the DC / AC conductivity.

The second direction makes use of holographic toy-models of momentum relaxation to construct self-consistent theories of hydrodynamic transport with slow or fast momentum relaxation. Holographic results are then matched and compared to phenomenological theories of hydrodynamics. We have also examined how Goldstone modes coming from spontaneous symmetry breaking, which normally give rise to divergent DC conductivities (superfluidity), can be given a finite lifetime by various relaxation mechanisms.

3. Description of the main results achieved so far

Our main results so far are
i. JHEP 1502 (2015) 035: The construction of gravitational geometries with intermediate scaling regions, which appear both in thermodynamics observables (like the entropy density) or in transport observables (optical conductivity). This demonstrates how Gauge/Gravity duality may be used to reproduce the phenomenology in high Tc superconductors, in particular the presence of mid-Infra Red quantum critical scalings as reported in Nature 425, 271-274 (2003) .
ii. JHEP 1501 (2015) 039: The demonstration of a qualitative match between hydrodynamic theories with slow momentum relaxation incorporated in a phenomenological way, and a self-consistent toy model of holographic momentum relaxation. We show that the dynamics is dominated by a Drude-like pole related to the magnitude of translation symmetry breaking and carefully match the spectrum of collective excitations of both approaches. When momentum relaxation is strong, we show that the dynamics is dominated by diffusion and study the crossover between the two regimes by tracking the quasi-normal modes of the black hole.
iii. JHEP 1509 (2015) 090: We unpack holographic formulae for thermoelectric DC conductivities and identify which part comes from momentum relaxation and from intrinsic, quantum critical dissipation. This resolved an outstanding confusion in the field in how the DC formulae, expressed in terms of data on the black horizon, should be interpreted on the boundary.
iv. JHEP 1510 (2015) 112: Drawing on our previous work in iii., we show how even in relativistic hydrodynamic, thermoelectric conductivities can be decomposed into a quantum critical contribution and a piece coming from momentum conservation. We match this to a holographic computation of the quantum critical conductivity in terms of horizon data, which moreover allows to predict its temperature dependence.
v. JHEP 1604 (2016) 122: Here we examine how thermoelectric DC conductivities are affected by next-to-leading order corrections in the effective field theory in the presence of momentum relaxation, by turning on higher derivative corrections to the two-derivative leading action. We show that lower bounds on the DC electric conductivity reported in the literature (Phys.Rev.Lett. 115 (2015) no.22, 221601) can be arbitrarily lowered by including these corrections. The magnitude of the corrections is limited by causality of the dual field theory.
vi. Phys.Rev. B94 (2016) no.5, 054502: Motivated by optical conductivity data in 2D disordered superfluid films showing the existence of metallic phases driven by tuning the magnetic field, we construct a hydrodynamic theory of quantum-fluctuating superconductivity. We give formulae for the optical and DC electric conductivities in terms of the superfluid phase relaxation rate. We also compute this rate when relaxation is due to moving vortices, reproducing previous results but in a fully quantum and transparent treatment.

4. Expected final results and their potential impact and use (including the socio-economic impact and the wider societal implications of the project so far)

At the end of the Fellowship, we expect to have made significant progress towards understanding hydrodynamic metallic transport and unconventional quantum criticality. Beyond the intrinsic interest of these results, they will provide important insight in the physics of real systems like the HTCs or GNCP. Both classes of materials are the subject of intensive research activity, due to their potential technological applications.

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Life Sciences
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