Bounding Transport and Chaos in Condensed Matter and Holography

20 Aug 2018, 09:00 → 14 Sept 2018, 18:00 Europe/Stockholm

122:026 (Nordita, Stockholm)

Blaise Goutéraux, Erez Berg (University of Chicago), Lárus Thorlacius (Iceland U. and Stockholm U.), Sean Hartnoll (Stanford University)

Venue

Nordita, Stockholm, Sweden

Scope This program will explore recent developments in describing the dynamics of strongly-coupled quantum systems using the notion of fundamental, quantum bounds on transport, and their interplay with quantum chaos. Experiments, as well as theoretical results coming from quantum field theory, lattice models and gauge/gravity duality, hint that the late time dynamics of these systems is governed by a Planckian timescale, the shortest allowed by quantum mechanics. This timescale provides a bound on the growth of chaos and the scrambling of quantum information, saturated in theories with Einstein holographic duals. From the point of view of thermoelectric transport, this timescale may bound the diffusive processes which underpin the ubiquitous T-linear resistivity of the bad metallic phase of high Tc superconductors and other unconventional materials. Diffusive transport also emerges in exactly solvable, quantum chaotic models like the Sachdev-Ye-Kitaev model. By bringing together international leaders in condensed matter and high energy physics, we aim at enhancing our current understanding by combining experimental results and the various theoretical, non-perturbative approaches to these problems. Participants will include experts in thermoelectric transport experiments, hydrodynamics, gauge/gravity duality, numerical and analytic condensed matter theory and conformal field theory. [Timetable - available from start of the program]

Download Poster or event logo

Application for participation to this program is open

Confirmed invited participants include

Kamran Behnia (ESPCI, Paris) Mike Blake (MIT) Sera Cremonini (Lehigh) Richard Davison (Harvard) Anatoly Dymarsky (Kentucky) Aristomenis Donos (Durham) Johannes Gooth (MPI Dresden) Saso Grozdanov (MIT) Nigel Hussey (Radboud U., Nijmegen) Nabil Iqbal (Durham) Kristan Jensen (San Francisco State U) Aharon Kapitulnik (Stanford) Elias Kiritsis (Crete and APC, Paris)

Pavel Kovtun (Victoria) Andy Lucas (Stanford) John McGreevy (UC San Diego) Andrew Mackenzie (MPI Dresden) Christiana Pantelidou (Durham) Tomaz Prosen (U. of Ljubljana) Thomas Scaffidi (Berkeley) Koenraad Schalm (Leiden) Peter Schauss (Princeton) Effrat Shimshoni (Bar-Ilan) Andrei Starinets (Oxford) Joseph Thywissen (Toronto)

Contact

cmh2018@nordita.org

Accommodation

Please be aware that unfortunately, scammers sometimes approach participants claiming to be able to provide accommodation and asking for credit card details. Please do not give this information to them. For successful applicants, Nordita will be in touch via email regarding accommodation. If you are in any doubt about the legitimacy of an approach, please get in contact with the organisers.

Sponsored by:

Monday, 20 August

1 Registration and coffee

2 Planckian Bound on the Decay of Simple Operators

I propose a generic Planckian bound on the lifetime of "simple" operators. This is related -- but not identical -- to the Planckian bound on quantum many-body chaos. This proposal reconciles the intuition that quantum dynamics (and chaos) is bounded by the Planckian time scale with the behavior of free theories, disordered metals in the low temperature limit, and disorder-driven metal-insulator transitions.

Speaker: Andrew Lucas (Stanford)

Slides Lucas.pdf

3 Space-Time in the SYK Model

Speaker: Kenta Suzuki (Ecole Polytechnique)

Slides Suzuki.pdf

4 Higher-form global symmetry in Theory of elasticity and holographic model with transverse sound

Speaker: Nick Poovuttikl (Iceland)

Slides Poovuttikul.pdf

Tuesday, 21 August

5 Fine Grained Chaos in AdS2 and AdS3

Speaker: Moshe Rozali (UBC)

Slides Rozali.pdf

6 Slow relaxation and diffusion in holographic quantum critical phases

In many-body quantum systems with strong interactions, the timescale governing transport is typically expected to be short and set by the inverse temperature. For example, in many holographic quantum critical phases of matter the thermal diffusivity (in appropriate units) is set by the inverse temperature. However, there are a simple class of such phases where this is not the case. I will discuss these phases and show that they have a collective excitation whose lifetime is parametrically longer than the inverse temperature. The lifetime of this excitation is enhanced due to its sensitivity to an irrelevant deformation, and I will show that it is this lifetime which ultimately governs the thermal diffusivity in these phases.

Speaker: Richard Davison (Harvard)

Slides Davison.pdf

7 Reception

Wednesday, 22 August

8 Origin of macroscopic Thouless (diffusion) time from the underlying quantum mechanics

Speaker: Anatoly Dymarsky (Kentucky)

Slides Dymarsky.pdf

9 Coffe break

10 What is a transport coefficient?

Speaker: Pavel Kovtun (University of Victoria)

Slides Kovtun.pdf

Thursday, 23 August

11 A theory of reparameterizations for AdS3 gravity

Speaker: Kristan Jensen (San Francisco State University)

Slides Jensen.pdf

12 Locality Bound for Dissipative Quantum Transport

Speaker: Xizhi Han (Stanford)

Slides Han.pdf

13 Holographic Strange Insulators from Pinning of Spontaneous Superstructures

When one considers the interplay between spontaneous and explicit symmetry breaking in finite charge density systems, one can observe the metal-insulator phase transition when the spontaneous superstructure is formed on top of the explicitly broken state. This goes under the name of "pinning of charge density wave" and eventually can lead to the formation of a Mott insulator, when the pinning gets strong. I will discuss the examples of this phenomenon in holographic models with periodic inhomogeneous and helical homogeneous lattices. The insulating state formed in these holographic models turns out to be quite interesting: firstly it is gapless and inherits the scaling features of the near horizon geometry, secondly, it demonstrates strong suppression of conductivity even for weak explicit translational symmetry breaking, which goes beyond the usual picture of the conductivity being governed by the momentum relaxation rate.

Speaker: Alexander Krikun (Leiden University)

Slides Krikun.pdf

Friday, 24 August

14 Holographic Fermions in Striped Superconductors

In this talk I will discuss a holographic model of a striped superconductor, in which a U(1) symmetry and translational invariance are broken spontaneously at the same time. This construction provides a concrete example of intertwined orders in holography, and realizes certain key features of pair density wave order. I will also examine the behavior of a probe fermion in this background and the formation and evolution of a Fermi surface in the corresponding PDW phase, in the presence of an explicit UV lattice. The structure of the Fermi surface is very sensitive to the strength of the lattice. In particular, strong lattice effects lead to a broadening of the spectral weight peaks and a gradual disappearance of the Fermi surface along the symmetry breaking direction. The resulting Fermi surface appears to consist of detached segments reminiscent of Fermi arcs.

Speaker: Sera Cremonini (Lehigh University)

Slides Cremonini.pdf

Monday, 27 August

15 Registration and coffee

16 Bad metallic transport in a modified Hubbard model

Strongly correlated metals often display anomalous transport, including T-linear resistivity above the Mott-Ioffe-Regel limit. We introduce a tractable microscopic model for bad metals, by supplementing the well-known Hubbard model --- with hopping t and on-site repulsion U --- with a `screened Coulomb' interaction between charge densities that decays exponentially with spatial separation. This interaction lifts the extensive degeneracy in the spectrum of the t=0 Hubbard model, allowing us to fully characterize the small t electric, thermal and thermoelectric transport in our strongly correlated model. Throughout the phase diagram we observe T-linear resistivity above the Mott-Ioffe-Regel limit, together with strong violation of the Weidemann-Franz law and a large thermopower that can undergo sign change.

Speaker: Connie Mousatov (Stanford)

Slides Mousatov.pdf

17 Many body chaos in QED3

Speaker: Julia Steinberg (Harvard)

18 Quantum Chaos, hydrodynamics and black hole scrambling

Speaker: Koenraad Schalm (Leiden University)

Slides Schalm.pdf

Tuesday, 28 August

19 Quantum chaos in a Rydberg atom system

Speaker: Yochai Werman (U. C. Berkeley)

Slides Werman.pdf

20 Reception

Wednesday, 29 August

21 Observation of Quantum Bounds in Spin Diffusivity

Speaker: Joseph Thywissen (University of Toronto)

Slides Thywissen.pdf

22 Thermal Transport Beyond the Mott-Ioffe-Regel Limit

The Boltzmann-Drude picture of electronic transport ceases to be valid when the electron mean-free-path becomes shorter than the Fermi wavelength. The Mott-Ioffe-Regel limit is defined where the two lengths are equal, and beyond it metallic transport becomes incoherent. Most experimental works have focused on the electronic transport, with the host crystal providing a phonon background. Here we report thermal diffusivity measurements that, together with the resistivity, give a full account of transport of charge and entropy. Utilizing a high-resolution photothermal apparatus, we study the thermal diffusivity of several cuprate systems in the regime where the quasiparticle picture fails for both electron and phonons. The inverse diffusivity at high temperature can be fitted with a temperature-linear form, where the slope term is set by a unique velocity and a Planckian relaxation time ~h/kBT, The constant term represents a quantum-diffusion constant separating incoherent transport from a regime with well-defined quasiparticles.

Speaker: Aharon Kapitulnik (Stanford)

Slides Kapitulnik.pdf

Thursday, 30 August

23 Hydrodynamic electron flows and Hall viscosity

In metallic systems of small enough size and sufficiently strong momentum-conserving scattering, the viscosity of the electron gas can become the dominant process governing transport. In this regime, momentum is a long-lived quantity whose evolution is described by an emergent hydrodynamical theory. Furthermore, breaking time-reversal symmetry leads to the appearance of an odd component to the viscosity called the Hall viscosity, which has attracted considerable attention recently due to its quantized nature in gapped systems but still eludes experimental confirmation. Based on microscopic calculations, we discuss how to measure the effects of both the even and odd components of the viscosity using hydrodynamic electronic transport in mesoscopic samples under applied magnetic fields.

Speaker: Thomas Scaffidi (U. C. Berkeley)

Slides Scaffidi.pdf

24 Experimental Searches for Electron Hydrodynamics

Speaker: Andrew Mackenzie (Max Planck Institute for Chemical Physics of Solids)

Slides Mackenzie.pptx

25 Nernst effect near a Superconductor-Insulator transition

Speaker: Efrat Shimshoni (Bar-Ilan University)

Slides Shimshoni.pdf

Friday, 31 August

26 Pole-skipping

Speaker: Saso Grozdanov (MIT)

Slides Grozdanov.pdf

27 Coffe break

28 Hydrodynamics with fluctuating broken translations

Speaker: Anna Karlsson (Institute for Advanced Study)

Slides Karlsson.pdf

29 Topological semimetals from holography

Speaker: Ya-Wen Sun (University of Chinese Academy of Sciences)

Slides Sun.pdf

Monday, 3 September

30 Registration and coffee

31 Introduction

Speaker: Sean Hartnoll (Stanford)

32 Bad Metallic Transport in a Cold Atom Fermi-Hubbard System

Probing the charge transport properties of quantum materials can reveal their unique microscopic properties. Weakly interacting systems such as Fermi liquids are well described by semiclassical Boltzmann transport, but strong interactions blur the particle-like behavior of charge carriers causing this picture to break down. Transport in strongly interacting quantum systems is poorly understood, but exhibits interesting phenomenology in many real materials. In our work, we experimentally study charge conductivity in the Fermi-Hubbard model. Using a quantum gas microscope, we impose a density modulation on a uniform system of ultracold 6Li in a 2D optical lattice and observe this modulation decay due to charge diffusion. We find that the decay can be described by a hydrodynamic model and extract the momentum relaxation rate and diffusion constant for a range of temperatures. We determine the conductivity from the diffusion constant using the Nernst-Einstein relation. We observe that the resistivity scales linearly with temperature and shows no sign of saturation for temperatures ranging from near the super-exchange energy scale to the bandwidth. These anomalous behaviors are characteristic of bad metals.

Speaker: Peter Schauss (Princeton University)

Slides Schauss.pdf

33 A quantum hydrodynamical description for chaos

Rapid progress in calculating out-of-time ordered correlation functions in holographic theories and solvable models like the Sachdev-Ye-Kitaev model has led to new characterisations of chaos in quantum many-body systems. However, a unified description of this behaviour is so far lacking. Here I will discuss a recent proposal for an effective field theory description of chaos in terms of `quantum hydrodynamics'. In this approach the scrambling of quantum information (i.e. chaos) arises from interactions between generic operators and hydrodynamic fluctuations.

Speaker: Michael Blake (MIT)

Slides Blake.pdf

Tuesday, 4 September

34 Hall number and other anomalies in the strange metal phase of overdoped cuprates

Speaker: Nigel Hussey (High Field Magnet Laboratory, Nijmegen)

Slides Hussey.pdf

35 Spectral form factor in an exactly solvable model of many body quantum chaos in 1+1 D

Speaker: Tomaz Prosen (University of Ljubljana)

Slides Prosen.pdf

36 Reception

Wednesday, 5 September

37 Phonons' Poiseuille flow

Speaker: Kamran Behnia (ESPCI, France)

Slides Behnia.pptx

38 Operator spreading and the emergence of dissipation in unitary dynamics with conservation laws

I will discuss the “scrambling” of local quantum information in chaotic quantum many-body systems in the presence of a locally conserved quantity like charge or energy that moves diffusively. The interplay between conservation laws and scrambling sheds light on the mechanism by which unitary quantum dynamics, which is reversible, gives rise to diffusive hydrodynamics, which is a dissipative process. Our results are obtained by examining the dynamics of operator spreading under unitary time evolution in a random quantum circuit model that is constrained to have a conservation law. We find that a generic spreading operator spreads ballistically with a front that moves at a “butterfly speed”, but develops a power law “tail” behind its leading ballistic front due to the slow dynamics of the conserved component of the operator. This structure implies that the out-of-time-order commutator (OTOC) between two initially spatially separated operators grows sharply upon the arrival of the ballistic front but, in contrast to systems with no conservation laws, it develops a diffusive tail and approaches its asymptotic late-time value only as a power of time instead of exponentially. I will also present these results within an effective hydrodynamic description which contains multiple coupled diffusion equations.

Speaker: Vedika Khemani (Harvard)

Slides Khemani.pdf

Thursday, 6 September

39 Bounds on transport and thermalization from positivity

Speaker: Luca Delacrétaz (Stanford)

Slides Delacretaz.pdf

40 Strange metals from local quantum chaos

Speaker: John Mcgreevy (UCSD)

Slides McGreevy.pdf

Friday, 7 September

41 Towards a comprehensive test of holographic principles in cuprates

Speaker: Erik Van Heumen (van der Waals-Zeeman institute, Amsterdam)

Monday, 10 September

42 Registration and coffee

43 Quantum fluctuations in real and complex Sachdev-Ye-Kitaev models

Speaker: Dmitry Bagrets (Institute for Theoretical Physics, University of Cologne)

Slides bagrets.pdf

44 Applications of higher form symmetries

Speaker: Nabil Iqbal (Durham University)

Slides iqbal.pdf

Tuesday, 11 September

45 Solvable models of correlated metals with interactions and disorder, and their transport properties

Despite much theoretical effort, there is no complete theory of the “strange” metal phase of the high temperature superconductors, and its linear-in-temperature resistivity. This phase is believed to be a strongly-interacting metallic phase of matter without fermionic quasiparticles, and is virtually impossible to model accurately using traditional perturbative field-theoretic techniques. Recently, progress has been made using large-N techniques based on the solvable Sachdev-Ye-Kitaev (SYK) model, which do not involve expanding about any weakly-coupled limit. I will describe constructions of solvable models of strange metals based on SYK-like large-N limits, which can reproduce some of the experimentally observed features of strange metals and adjoining phases. These models, and further extensions, could possibly pave the way to developing a controlled theoretical understanding of the essential building blocks of the electronic state in correlated-electron superconductors near optimal doping.

Speaker: Aavishkar Patel (Harvard)

Slides patel.pdf

46 Towards bad metallic transport from holographic failed insulators

Speaker: Daniel Arean (IFT, Madrid)

Slides arean.pdf

47 Reception

Wednesday, 12 September

48 Interpolating between strong and weak coupling in thermal QFTs with gravity duals

Speaker: Andrei Starinets (University of Oxford)

Slides starinets.pdf

49 Electrical transport near Ising-nematic QCP

An electronic nematic order spontaneously breaks the rotation symmetry of many body system, making various physical properties anisotropic. It has been observed in various systems, in particular the cuprate and iron-based high temperature superconductors. In the vicinity of a nematic quantum critical point — achieved by tuning some external parameter such as pressure or doping — the physics is described by that of low-frequency long-wavelength order parameter fluctuations coupled to a Fermi surface. However, due to the momentum-conserving nature of the induced electron-electron interaction, the temperature dependence of the resistivity near an Ising nematic QCP remains unclear. In this talk, we shed light on the problem by incorporating disorder and Umklapp process into the low-energy theory. Our work can be viewed as solving an extended Boltzmann equation, with a collision integral that accounts for complicated multi-particle scattering processes important near the QCP.

Speaker: Xiaoyu Wang (James Frank Institute, University of Chicago)

Slides wang.pdf

50 Entanglement entropy in generalised Quantum Lifshitz models

n the initial part of the talk I will review the generalised quantum Lifshitz models, that is free field theories with Lifshitz scaling symmetry which extend the (2+1)-dimensional quantum Lifshitz model to higher dimension. As in the lower dimensional case the ground state wave functional is invariant under spatial conformal symmetries, whenever the dynamical critical exponent is equal to the number of spatial dimensions. Thanks to this feature, they provide us with simple models for non-relativistic critical theories, suitable to investigate the scaling properties of entanglement entropy. I will then outline the computation of the sub-leading universal terms in the entanglement entropy for spherical entangling hyper-surfaces in these theories, and discuss the results.

Speaker: Valentina Giangreco Puletti (University of Iceland)

Thursday, 13 September

51 Holographic Abrikosov lattice

Speaker: Christiana Pantelidou (Durham University)

Slides pantelidou.pdf

52 Instabilities of 2d quantum critical metals in the Nf->0 limit

We study a Fermi surface coupled to fluctuations of a critical order parameter in 1+2 dimensions. The limit of vanishing fermion flavor number gives a controlled way of studying this strongly coupled theory. In this talk I show how to calculate charge, spin and pairing susceptibilities in this limit and find that the critical fluctuations induce charge/spin density wave order or pairing for come ranges of parameters. We show that adding some of the Nf corrections does not change the range of parameters where these instabilities show up.

Speaker: Petter Saterskog (Nordita)

Slides petter.pdf

53 Holographic tensor models

Speaker: Nicolas Delporte (LPT Orsay)

Slides delporte.pdf

Friday, 14 September

54 Transport and Black Hole Horizons

Speaker: Aristomenis Donos (Durham University)

Slides Donos.pdf

55 Holographic Plasmons

Plasmons are ubiquitous in all conducting compounds. We show how to model plasmons holographically, relevant for systems without quasiparticles, e.g. the ‘strange metal’ phase of high temperature superconductors. By introducing holographic electromagnetism we derive a novel set of of boundary conditions which the plasmon modes, and in fact all physical modes, must satisfy. We present the results for both bulk and 2DEG plasmons, and highlight that holographic bulk plasmons exhibit an exotic dispersion in a part of the parameter space not accessible by other methods.

Speaker: Ulf Gran (Chalmers)

Slides gran.pdf

56 Need for sound speed and holography

Several works in holography has lent support on the conjecture that there could be a universal speed limit for the sound set by the conformal value. Further support comes from kinetic theory and QCD. Yet, there are many instances violating this bound. I furthermore present several holographic models that break the speed barrier and discuss their common denominator.

Speaker: Niko Jokela (University of Helsinki)

Slides jokela.pdf