Holographic Quantum Matter 2018

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    A strongly correlated metal from coupled SYK models
    (2018-05) Balents, Leon
    We show how a strongly correlated Fermi liquid can be described by coupling together a lattice of SYK models.
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    Sine-Square deformation of conformal field theory
    (2018-05) Ryu, Shinsei
    By making use of conformal mapping, we construct various time-evolution operators in (1+1) dimensional conformal field theories (CFTs) deformed by some envelope function. Examples of such deformed evolution operators include the entanglement Hamiltonian, and the so-called sinesquare deformation of the CFT. Within our construction, the spectrum and the (finite-size) scaling of the level spacing of the deformed evolution operator are known exactly. Based on our construction, we also propose a regularized version of the sine-square deformation, which, in contrast to the original sine-square deformation, has the spectrum of the CFT defined on a spatial circle of finite circumference L, and for which the level spacing scales as 1/L2, once the circumference of the circle and the regularization parameter are suitably adjusted.
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    Computing quantum thermalization dynamics: from quantum chaos to emergent hydro
    (2018-05) Altman, Ehud
    Computing the dynamics of strongly interacting quantum systems presents a fundamental challenge due to the growth of entanglement entropy in time. I will describe a new approach that overcomes this obstruction and captures chaotic dynamics and emergent hydrodynamic transport of quantum systems. Our scheme utilizes the time dependent variational principle with matrix product states to truncate “non-useful” entanglement. I will present new insights, obtained using the variational scheme, on quantum chaos on tensor networks, as well as new results pertaining to the many-body localization transition. If time permits I will offer an alternative perspective on the relation between quantum and classical chaos in many body systems, using a classical version of the Sachdev-Ye- Kitaev model. Chaos in this model is related to diverging geodesics on a SO(N) manifold equipped with a random metric. The quantum bound on chaos arises from a “chaotic mobility edge” in the classical Lyapunov spectrum, separating the lower part of the spectrum for which a classical chaos picture applies from the higher part of the spectrum for which quantum interference effects are strong enough to kill classical chaos.
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    Space-Time in the Sachdev-Ye-Kitaev Model
    (2018-05) Jevicki, Antal
    The question of the bulk space-time in the Sachdev-Ye-Kitaev model will be discussed . Starting with the basic issue regarding its signature a bi-local map will be described to reach the bulk. Physical properties of the SYK spectrum will be discussed.
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    On the Geometry of the Firewall Partially mixed states in SYK
    (2018-05) Verlinde, Herman
    In this talk, I introduce and study a class of entangled states in the SYK model, that interpolate between the thermo-field double and a disentangled product of two pure states. The proposed holographic dual geometry consists of two black hole geometries separated by a domain wall. I explain why this wall represents the location of the firewall, that limits the reach of the holographic bulk reconstruction.
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    Spectral Properties of the SYK Model
    (2018-05) Verbaarschot, Jacobus
    The Sachedev-Ye-Kitaev model provides us with a new window on strongly interacting many-body systems. In particular, it is a variant of the two-body random ensemble which captures the main features of nuclear interactions. One of main successes of recent work on the SYK model is that it shows that the Bethe formula for the nuclear level density is a direct consequence of the conformal symmetry of the low-energy sector of this model. We study the spectrum of the q-body SYK model by means of the moment method, and have obtained analytical results for all moments up to order 1/ N^3 in the number of Majorana fermions N. We elucidate the structure of the moments and how they relate to the free energy including $1/q$ corrections. For fixed $q^2/N$, the spectral density is given by the weight function of the Q-Hermite polynomials, which for large $N$ and $q$ simplifies to $exp( -N arcsin^2(E/E_0) / q^2)$. This spectral form reproduces the free energy obtained by path integral methods in the same limit. From applications to nuclear physics, it is clear that the SYK model has to be chaotic, which is also one of the main reasons why it is of interest to black hole physics. We study the chaotic dynamics by means of the number variance and the closely related spectral form factor. We show that the asymptotic quadratic dependence of the number variance results in a $1/t^2$ peak of the spectral form factor for short times, while random matrix spectral statistics is found for longer time scales.
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    Two studies of entanglement in the SYK
    (2018-05) Gu, Yingfei
    In this talk I will first talk about the eigenstate entanglement in the SYK model and then talk about the spread of Renyi entanglement entropy between two halves of a SYK chain, prepared in a thermofield double state.
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    Strange metals from local quantum chaos
    (2018-05) McGreevy, John
    How to make a controlled model of a non-Fermi-liquid metal with efficient current dissipation is a long-standing problem. Results from holographic duality suggest a framework where local critical fermionic degrees of freedom provide both a source of decoherence for the Landau quasiparticle, and a sink for its momentum. This leads us to study various Kondo-lattice-type models with Sachdev- Ye-Kitaev models in place of the spin impurities. Several interesting strange metals are found.
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    Z2 fractionalized phases of t-J models
    (2018-05) Sachdev, Subir
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    Quantum ergodicity in the SYK model
    (2018-05) Bagrets, Dmitry
    In my talk I will discuss a replica path integral approach describing the quantum chaotic dynamics of the SYK model at large time scales [1]. The theory leads to the identification of non-ergodic collective modes which relax and eventually give way to an ergodic long time regime describable by random matrix theory (RMT). These modes, which play a role conceptually similar to the diffusion modes of dirty metals, carry quantum numbers which can be identified as the generators of the Clifford algebra: each of the 2^N different products that can be formed from N Majorana operators defines one effective mode. The competition between a decay rate quickly growing in the order of the product and a density of modes exponentially growing in the same parameter explains the characteristics of the system’s approach to the ergodic long time regime. I will present a number of analytical results for various spectral correlation functions which characterise the dynamics of the SYK model and demonstrate their favorable agreement with existing numerical data. [1] A. Altalnd and D. Bagrets, Nucl. Phys. B 930, 45-68 (2018)
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    Towards the AdS dual of SYK
    (2018-05) Rosenhaus, Vladimir
    The SYK model and its variants are a novel class of solvable large N theories. We discuss the calculation of all large N correlation functions and the implications for the bulk dual.
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    BOUNDARY DUAL OF THE BULK SYMPLECTIC FORM
    (2018-05) Sárosi, Gábor
    I will discuss the quantum Kahler structure, induced by the Fubini-Study metric, on the space of complexified Euclidean sources in holographic conformal field theories. I will show that the quantum Kahler form is identical with the symplectic form of canonical gravity in the bulk. I will discuss some possible applications of this observation, in particular a boundary prescription to calculate the variation of the volume of a maximal slice.
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    How to make a wormhole Understanding global AdS2
    (2018-05) Maldacena, Juan
    We discuss the physics of two coupled SYK models and its relation to traversable wormholes involving nearly AdS_2 spacetimes.