# Many-Body Quantum Chaos, Bad Metals and Holography

Europe/Stockholm
E306 and P216 (SU campus)

, , ,
Description

### Venue

The workshop is organized by Nordita, Stockholm, Sweden, and will be held in the Arrhenius Lab on the Frescati Campus of Stockholm University, just north of Nordita. See this Map of Frescati Campus where the routes from the subway station to the lecture halls E306 and P216 and the campus restaurant are shown.

### Scope

The workshop will provide a forum for discussing recent cross-disciplinary advances in describing the dynamics of strongly-coupled many-body systems using notions from condensed matter, quantum chaos and holography. Emphasis will be placed on the impact on transport of fundamental bounds and the explicit/spontaneous breaking of symmetries. We will draw lessons on transport without quasiparticles, relevant both for theoretical models (e.g. holography, Sachdev-Ye-Kitaev) and experiments on bad metals and high Tc superconductors. This three-day event will bring together international leaders in condensed matter physics and high energy theory.

This workshop is supported by the Royal Swedish Academy of Sciences through its Nobel Institute for Physics, the Wenner-Gren Foundation and Nordita.

Timetable

### Format

The meeting starts at 9.00 am on Wednesday and ends at 5.00 pm on Friday.

### Invited speakers

 Matteo Baggioli (Crete U.) Jens Bardarson (KTH) Mike Blake (MIT) Sera Cremonini (Lehigh U.) Richard Davison (Harvard U.) Balázs Dóra (Budapest U.) Lara Faoro (U. Pierre et Marie Curie Paris 6) Saso Grozdanov (MIT) Razvan Gurau (École Polytechnique) Oscar Henriksson (U. of Helsinki) Niko Jokela (U. of Helsinki) Alexander Krikun (Leiden U.) Andy Lucas (Stanford) Raghu Mahajan (IAS) Daniele Musso (Santiago de Compostella) Aurelio Romero-Bermudez (Leiden U.) Christopher Rosen (Imperial College) Christiana Pantelidou (Durham U.) Koenraad Schalm (Leiden U.) Petter Säterskog (Nordita) Julian Sonner (U. of Geneva) Watse Sybesma (Utrecht) Jan Zaanen (Leiden U.) Vaios Ziogas (Durham U.)

### Application

If you want to participate in the workshop, please fill in the application form. For further information please visit the page Application.

There is no registration fee, but application is mandatory due to strict space limitations.

Application deadline: 1 September 2017, 16:00 CEST

### Travel Reimbursement

PhD students and junior postdoctoral fellows are eligible to apply for travel and accommodation grants to participate in the workshop. If you are interested in such a grant, please register before August 4 and mark the corresponding field in the application form, briefly summarize your interest in the program in the comments field, and indicate an estimation of your expected travel expenses. Since only a limited number of grants is available, decision concerning the grants will be made on a case-by-case basis and you will be notified shortly after the application deadline.

### Accommodation

Nordita can book a limited number of rooms in the Stockholm apartment hotel BizApartments at a discounted rate, or at Matsällskapet Guestrooms. If you are interested in booking one of these rooms, you should register before August 4 and tick the corresponding box in the application form.

Further options for accommodation close to the conference venue can also be found under Accommodation.

### Contact

mbqc2017@nordita.org

### Sponsored by:

• Wednesday, October 4
• 1
Diffusion and Chaos in Quantum Matter E306

### E306

#### SU campus

In this talk I will discuss recent developments that have suggested new connections between the transport properties of quantum matter and many-body chaos. In particular I will describe how in many holographic theories there are simple relationships between the thermoelectric diffusion constants and the butterfly velocity, which describes the speed at which chaos propagates.
Speaker: Mike Blake (MIT)
• 2
Thermal diffusivity and chaos in holographic theories E306

### E306

#### SU campus

I will show that the thermal diffusivity is closely related to the butterfly velocity and the Lyapunov exponent in a large class of holographic theories at low temperature. I will explain how this is a consequence of the fact that the thermal conductivity in these theories depends only on the metric near the horizon of the dual black hole, and is otherwise independent of the matter fields and their profiles.
Speaker: Richard Davison
• 3
Coffee break Outside E306

### Outside E306

#### SU campus

• 4
An upper bound on transport E306

### E306

#### SU campus

The linear growth of operators in local quantum systems leads to an effective lightcone even if the system is non-relativistic. We show that consistency of diffusive transport with this lightcone places an upper bound on the diffusivity: D<=v^2 \tau_eq. The operator growth velocity v defines the lightcone and \tau_eq is the local equilibration timescale, beyond which the dynamics of conserved densities is diffusive. We verify that the bound is obeyed in various weakly and strongly interacting theories. In holographic models this bound establishes a relation between the hydrodynamic and leading non-hydrodynamic quasinormal modes of planar black holes. Our bound relates transport data --- including the electrical resistivity and the shear viscosity --- to the local equilibration time, even in the absence of a quasiparticle description. In this way, the bound sheds light on the observed T-linear resistivity of many unconventional metals, the shear viscosity of the quark-gluon plasma and the spin transport of unitary fermions.
Speaker: Raghu Mahajan (IAS)
• 5
Hydrodynamic Modes of Incoherent Black Holes E306

### E306

#### SU campus

In this talk I will consider transport of conserved charges in strongly coupled quantum systems with broken translations, using holographic techniques. Such systems are relevant in condensed matter physics in the context of spontaneous symmetry breaking as well as in the context of momentum relaxation through a lattice. In this setup of reduced symmetry, I will give the precise identification of the relevant hydrodynamic modes that diffuse heat and electric charge. As an aside, in the case of explicit breaking I will connect with previous results of DC conductivities from black holes horizons via an Einstein relation for the diffusion constants.
Speaker: Vaios Ziogas (Durham University)
• 6
Holographic doped Mott insulator E306

### E306

#### SU campus

As soon as one considers the holographic model with spontaneous translation symmetry breaking on top of the background, which posses explicit modulation of the chemical potential, one encounters a broad range of interesting physical phenomena related to the commensurate lock in between these two spacial structures. I will show that in this holographic framework one can relyiably address the physics of Mott insulator and consider the discommensuration lattices and stripes, which arise when the Mott insulator is "doped".
Speaker: Alexander Krikun (Leiden University)
• 7
Lunch break Restaurant Lantis

### Restaurant Lantis

#### SU campus

• 8
The melonic universality class E306

### E306

#### SU campus

Random Tensors generalize random matrices to higher dimensions. In the large N limit random tensors exhibit a new universal behavior dominated by melonic graphs. In this talk I will review the basics of Random Tensor theory and discuss this new universal behavior.
Speaker: Gurau Razvan (Ecole Polytechnique and CNRS)
• 9
Stability of chaos in a generalised SYK model E306

### E306

#### SU campus

I will show that a generalised SYK model with an additional one-body infinite-range random interaction, which is a relevant perturbation in the infrared, is still quantum chaotic for a fixed value of the perturbation and sufficiently high temperature. I will also show that, at low temperature, this model shows a chaotic-to-integrable transition. [arXiv:1707.02197]
Speaker: Aurelio Romero-Bermudez (Leiden University)
• 10
Coffee break Outside E306

### Outside E306

#### SU campus

• 11
Compressible quark matter in N=4 SYM E306

### E306

#### SU campus

I will discuss the holographic dual of strongly coupled, four-dimensional SYM with massless flavour in the Veneziano limit at finite quark density and finite temperature. The fundamental degrees of freedom are modelled by a distribution of D7-branes with a non-vanishing electric field on their worldvolume that backreacts on the geometry of a stack of colour D3-branes. I will present the RG flows corresponding to this system discuss the thermodynamics of the system.
Speaker: Christiana Pantelidou (Durham University)
• 12
Social event Nordita West, Roslagstullsbacken 17, Room 122:026 (Nordita West, Roslagstullsbacken 17)

### Nordita West, Roslagstullsbacken 17, Room 122:026

#### Nordita West, Roslagstullsbacken 17

• Thursday, October 5
• 13
Thermalisation of pure states E306

### E306

#### SU campus

In this talk I will present some recent progress in studying thermalisation in low-dimensional systems with holographic duals. Firstly I will describe first-principles field theory calculations in pure states dual to collapsing black holes, highlighting the role of non-perturbative corrections in the information-loss problem. Secondly, I will show how eigenstate thermalisation supplies a unifying perspective on many aspects of holographic thermalisation, and in particular on the relation between pure states and bulk geometry.
Speaker: Julian Sonner
• 14
A Holographic Model for the Anomalous Scalings of the Cuprates E306

### E306

#### SU campus

In this talk I will examine transport in a holographic model in which the dynamics of the charged degrees of freedom is described by the non-perturbative Dirac--Born--Infeld (DBI) action. The generic structure of the DC conductivity matrix for these theories is extremely rich. When the momentum relaxation is strong, the model reproduces the anomalous temperature dependence of the resistivity and Hall angle of the cuprate strange metal. These scaling laws would not be present without the non- linear dynamics encoded by the DBI interactions. This model provides explicit examples in which transport is controlled by different relaxation times. On the other hand, when only one quantity sets the temperature scale of the system, the Hall angle and DC conductivity typically exhibit the same temperature behavior. I illustrate this point with new fully-backreacted dyonic black brane solutions.
Speaker: Sera Cremonini
• 15
Coffee break Outside E306

### Outside E306

#### SU campus

• 16
There and Back: RG Boomerangs from Spatially Modulated Deformations E306

### E306

#### SU campus

Renormalization group flows between fixed points provide a powerful framework for both exploring and cataloging the myriad ways in which field theories can behave at low energies. Under favorable conditions, the physics of such flows can be reformulated geometrically, and examined in the context of gauge/gravity duality. I will discuss an interesting class of such flows, driven by carefully tuned spatially modulated deformations of a UV fixed point. This deformation can result in a "boomerang" RG flow, in which the theory returns to itself at low energies (with a renormalization of length scales). For sufficiently large deformations, the flow can exhibit intermediate energy scaling regimes along its journey to the IR fixed point. A “top-down” holographic description of this trajectory can be realized as a new solution to D=11 supergravity which deforms the AdS_4 x S^7 vacuum in a peculiar way.
Speaker: Christopher Rosen
• 17
Holographic studies of ABJM theory at finite density E306

### E306

#### SU campus

Adherence to a strict top-down framework in holography imposes tight constraints when computing for example fermionic spectral weights. I will discuss some holographic computations in finite density ABJM theory where these constraints translate into interesting physical properties, such as Fermi surfaces, without well-defined quasiparticles, that become gapped when the U(1) charge symmetry is broken. I then discuss the computation of the static charge susceptibility in a particular finite density state of ABJM theory, leading to a quantitative comparison between fermionic and bosonic correlators made possible by the top-down setup.
Speaker: Oscar Henriksson
• 18
Hydrodynamics for ideal fluids without boosts E306

### E306

#### SU campus

Many materials that behave as so-called non-relativistic fluids with strong interactions exhibit interesting properties, such as non-conventional superconductivity and superfluidity. The fact that non-relativistic fluids do not necessarily allow for boost symmetries poses a problem for making predictions using hydrodynamics, in which normally Lorentz or Galilean boosts are assumed. Me and my collaborators generalized the framework of hydrodynamics to work beyond situations where there is a boost symmetry. I will talk about this framework. As a proof of principle, I will compute the speed of sound for a gas of Lifshitz particles, which is a realization of a non-relativistic fluid without boost symmetry. If time permits I will cover some beyond ideal fluid results.
Speaker: Watse Sybesma
• 19
Lunch break Restaurant Lantis

### Restaurant Lantis

#### SU campus

• 20
Adiabatic continuity and Fermi-liquid like features in many-body localization E306

### E306

#### SU campus

The emergent integrability of the many-body localized phase can be understood in terms of localized quasiparticles. As a result, the occupations of the one-particle density matrix in eigenstates show a Fermi-liquid like discontinuity. Furthermore, in the steady state reached at long times after a global quench from a perfect density wave state, this occupation discontinuity is absent but the full occupation function remains strongly nonthermal. We discuss how one can understand this as a consequence of the local structure of the density wave and the resulting partial occupation of quasiparticles. Phenomenologically, this is reminiscent of the effect of temperature in Fermi liquids that results in smearing of the occupation function.
Speaker: Jens Bardarson
• 21
Boson-dominated quantum critical metals at Lorentz symmetric point E306

### E306

#### SU campus

We study the strongly coupled theory of a Fermi surface in 2+1 dimensions coupled to a massless scalar in a general limit in which fermionic loops are suppressed such as a matrix large $N$ limit or a vector small $N_f$ limit. The case where the Fermi velocity equals the boson velocity gives extra symmetry to the low energy limit of all diagrams which allows us to make general statements about the full fermion two-point function. We find that these theories generally have a non-monotonic dispersion across the Fermi surface resulting in splitting of the Fermi surface.
Speaker: Petter Säterskog
• Flash talks E306

### E306

#### SU campus

• 22
Generalised global symmetry and holography of dynamical extended objects E306

### E306

#### SU campus

I will discuss the concept of generalised global symmetry, which describe the conservation law associated to dynamical extended objects, and their implementation in holography. I will also discuss its application in the effective theory of matter in the presence of strong dynamical magnetic field as well as the incommensurate phase which breaks the translational symmetry spontaneously
Speaker: Nick Poovuttikul
• 23
Ward identities and relations between conductivities and viscosities in holography E306

### E306

#### SU campus

We derive relations between viscosities and momentum conductivity in 2 + 1 dimensions by finding a generalization of holographic Ward identities for the energy-momentum tensor. The generalization is novel in the sense that it goes beyond the usual identities obtained from holographic renormalization. Our results are consistent with previous field theory analysis. The main tools we use are a constant ‘probability current’ in the gravity dual, that we are able to define for any system of linear ODEs, and parity symmetry.
Speaker: David Rodríguez
• 24
Rindler Fluid with Weak Momentum Relaxation E306

### E306

#### SU campus

We realize the weak momentum relaxation in Rindler fluid, which lives on the time-like cutoff surface in an accelerating frame of flat spacetime. The translational invariance is broken by massless scalar fields with weak strength. Both of the Ward identity and the momentum relaxation rate of Rindler fluid are obtained, with higher order correction in terms of the strength of momentum relaxation. The Rindler fluid with momentum relaxation could also be approached through near horizon limit of the “cutoff AdS fluid” with momentum relaxation, which lives on a finite time-like cutoff surface in Anti-de Sitter(AdS) spacetime, and further could be connected with the holographic fluid living on AdS boundary at infinity. I will also update our recent progress on the holographic transports in Rindler Fluid.
Speaker: Yun-Long Zhang
• 25
Coffee break Outside E306

### Outside E306

#### SU campus

• 26
Holography and Experimental Quantum Matter E306

### E306

#### SU campus

A number of very recent experiments on strange metals in the cuprates have again highlighted the anomalous behavior of these materials compared to ordinary Fermi-liquid metals. Almost too good to be true, the displayed behavior shows remarkable similarities with the qualitative predictions from holography. I will briefly review these experiments probing the single electron spectrum, charge transport linear-in-T resistivity, charge density waves and their independence on doping, and density-density correlations. For each I will highlight why the results correspond with the predictions of holography based on a quantum critical state coexisting with order.
Speaker: Koenraad Schalm
• 27
Social event Nordita West, Roslagstullsbacken 17, Room 122:026 (Nordita West, Roslagstullsbacken 17)

### Nordita West, Roslagstullsbacken 17, Room 122:026

#### Nordita West, Roslagstullsbacken 17

• Friday, October 6
• 28
Quantum thermalization in holography and the laboratory P216

### P216

#### SU campus

The simple moral of eigenstate thermalization is that what we think is the rattling of classical things producing heat is a delusion caused by our incapacity to keep track of the flow of quantum information in the enormous many-body Hilbert space. Are there circumstances where it is impossible to construct such a consistent classical metaphor? Helped by holography we stumbled recently into a number of cases. Even in the elementary physics of expanding cold atom clouds a vivid example has been identified (arXiv:1703.02489). Planckian dissipation is in this regard a no-brainer but its ultimate consequence for experiment turns out to be stunningly weird (unpublished). Finally, the holographic incarnation of optical pump-probe experiments predicts that strange metals should invariably exhibit the phenomenon of instantaneous thermalization. I will argue that this suggests a critical test of the UV independence notion by mobilizing condensed matter experiment (arXiv:1708.08279).
Speaker: Jan Zaanen
• 29
Holographic pinning in probe brane models P216

### P216

#### SU campus

In a holographic probe-brane model exhibiting a spontaneously spatially modulated CDW+SDW ground state, I will introduce explicit sources of symmetry breaking in the form of ionic and antiferromagnetic lattices. I will demonstrate pinning, in which the translational Goldstone mode is lifted by the introduction of explicit sources of translational symmetry breaking. The numerically computed optical conductivity fits very well to a Drude-Lorentz model with a small residual metallicity, precisely matching analytic formulas for the DC conductivity. I also demonstrate an instability of the striped phase in the presence of a large- amplitude ionic lattice.
Speaker: Niko Jokela
• 30
Coffee break Outside P216

### Outside P216

#### SU campus

• 31
Hydrodynamics, magnetohydrodynamics from generalised global symmetries and the holographic butterfly effect P216

### P216

#### SU campus

In my talk, I will discuss various topics that will revolve around the subject of hydrodynamics. The first part of the talk will begin with a general discussion of hydrodynamics, its breakdown at weak coupling and the connection between hydrodynamics and many-body chaos. In particular, I will argue that at strong coupling, the holographic butterfly effect can be understood in terms of a hydrodynamic sound mode instability. In the second part of the talk, I will discuss a recent reformulation of magnetohydrodynamics and a construction of its holographic dual by using the concept of generalised global symmetries.
Speaker: Saso Grozdanov
• 32
Constraints on hydrodynamics from many-body quantum chaos P216

### P216

#### SU campus

Quantum chaos describes the dynamics of a many-body system at the onset of thermalization, while hydrodynamics describes the late time dynamics after thermalization has occurred locally. Consistency between these two descriptions provides constraints linking hydrodynamic data such as diffusion constants and sound speeds to quantum chaos. I will show that in large N quantum field theories, hydrodynamic coefficients are bounded by a light cone velocity: the speed at which the region where quantum scrambling has just begun expands. Under certain circumstances, including small N, this light cone velocity can be replaced by the butterfly velocity: the speed at which the region where quantum information has completely scrambled expands. Using these bounds I will predict two unexpected features of holographic models: (i) the inequivalence of light cone and butterfly velocities in many theories; (ii) the breakdown of the hydrodynamic gradient expansion at very long wavelengths in certain charge neutral plasmas.
Speaker: Andrew Lucas (Stanford University)
• 33
Lunch break Restaurant Lantis

### Restaurant Lantis

#### SU campus

• 34
AdS/CMT and (pseudo)symmetry breaking P216

### P216

#### SU campus

Holography provides models where internal and spacetime symmetries can be explicitly broken, yet the breaking is dominated by the spontaneous generation of a symmetry- breaking VEV. The characterization and actual computation of low-energy correlators reveals the dynamical detail of (pseudo)Nambu-Goldsotne modes and accounts for generic features of CMT systems such as the low-frequency structure of transport properties in bad metals.
Speaker: Daniele Musso
• 35
Elasticity and (pseudo)-phonons in holography P216

### P216

#### SU campus

We discuss the presence and the physical features of (pseudo)-phonons in the context of ''solid'' holographic massive gravity theories. We present a bottom-up model exhibiting for the first time in holography (gapped and damped) transverse phonons. We compute the elastic modulus and we determine the shear sound speed which turns out to be in good agreement with the theoretical expectations. We finally speculate on possible applications to viscoelastic materials.
Speaker: Matteo Baggioli
• 36
Coffee break Outside P216

### Outside P216

#### SU campus

• 37
Out-of-time-ordered density correlators in Luttinger liquids P216

### P216

#### SU campus

Information scrambling and the butterfly effect in chaotic quantum systems can be diagnosed by out-of-time-ordered (OTO) commutators through an exponential growth and large late time value. We show that the latter feature shows up in a strongly correlated many-body system, a Luttinger liquid, whose density fluctuations we study at long and short wavelengths, both in equilibrium and after a quantum quench. We find rich behaviour combining robustly universal and non-universal features. The OTO commutators display temperature and initial state independent behaviour, and grow as t2 for short times. For the short wavelength density operator, they reach a sizeable value after the light cone only in an interacting Luttinger liquid, where the bare excitations break up into collective modes. We benchmark our findings numerically on an interacting spinless fermion model in 1D, and find persistence of central features even in the non- integrable case. As a non-universal feature, the short time growth exhibits a distance dependent power.
Speaker: Balazs Dora
• 38
Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves P216

### P216

#### SU campus

In a chaotic classical system a small perturbation leads to the exponential divergence of trajectories characterized by Lyapunov time. As a result, the observables in two copies of the system experiencing different perturbations quickly become uncorrelated. In a many body system a local perturbation initially destroys the correlations locally, then the region where the correlations are destroyed quickly grows with time. This phenomena is known as butterfly effect. The concept of butterfly effect can be generalized to a closed chaotic quantum system even though such generic system does not necessarily have a direct analogue of Lyapunov divergence of trajectories because quantum mechanics prohibits the infinitesimal shift of the trajectory. The convenient measure of the butterfly effect is provided by the out-of-time-order correlator (OTOC) . In this work, we extend the Keldysh technique to enable the computation of OTOC. We show that the behavior of these correlators is described by equations that display initially an exponential instability which is followed by a linear propagation of the decoherence between two initially identically copies of the quantum many body systems with interactions. At large times the decoherence propagation (quantum butterfly effect) is described by a diffusion equation with non-linear dissipation known in the theory of combustion waves. The solution of this equation is a propagating non-linear wave moving with constant velocity despite the diffusive character of the underlying dynamics. Our general conclusions are illustrated by the detailed computations for the specific models describing the electrons interacting with bosonic degrees of freedom (phonons, two-level-systems etc.) or with each other.
Speaker: Lara Faoro