arXiv subjects

Jan de Boer

Publications and source records attributed to Jan de Boer.

At least 55 records · Page 3Linked to original sources

arXiv2019

Geometric Aspects of Holographic Bit Threads

We revisit the recent reformulation of the holographic prescription to compute entanglement entropy in terms of a convex optimization problem, introduced by Freedman and Headrick. According to it, the holographic entanglement entropy associated to a boundary region is given by the maximum flux of a bounded, divergenceless vector field, through the corresponding region. Our work leads to two main results: (i) We present a general algorithm that allows the construction of explicit thread configurations in cases where the minimal surface is known. We illustrate the method with simple examples: spheres and strips in vacuum AdS, and strips in a black brane geometry. Studying more generic bulk metrics, we uncover a sufficient set of conditions on the geometry and matter fields that must hold to be able to use our prescription. (ii) Based on the nesting property of holographic entanglement entropy, we develop a method to construct bit threads that maximize the flux through a given bulk region. As a byproduct, we are able to construct more general thread configurations by combining (i) and (ii) in multiple patches. We apply our methods to study bit threads which simultaneously compute the entanglement entropy and the entanglement of purification of mixed states and comment on their interpretation in terms of entanglement distillation. We also consider the case of disjoint regions for which we can explicitly construct the so-called multi-commodity flows and show that the monogamy property of mutual information can be easily illustrated from our constructions.

hep-th↗

arXiv2019

Holographic Schwinger-Keldysh effective field theories

We construct a holographic dual of the Schwinger-Keldysh effective action for the dissipative low-energy dynamics of relativistic charged matter at strong coupling in a fixed thermal background. To do so, we use a mixed signature bulk spacetime whereby an eternal asymptotically anti-de Sitter black hole is glued to its Euclidean counterpart along an initial time slice in a way to match the desired double-time contour of the dual field theory. Our results are consistent with existing literature and can be regarded as a fully-ab initio derivation of a Schwinger-Keldysh effective action. In addition, we provide a simple infrared effective action for the near horizon region that drives all the dissipation and can be viewed as an alternative to the membrane paradigm approximation.

hep-th↗

arXiv2019

A Modular Sewing Kit for Entanglement Wedges

We relate the Riemann curvature of a holographic spacetime to an entanglement property of the dual CFT state: the Berry curvature of its modular Hamiltonians. The modular Berry connection encodes the relative bases of nearby CFT subregions while its bulk dual, restricted to the code subspace, relates the edge-mode frames of the corresponding entanglement wedges. At leading order in 1/N and for sufficiently smooth HRRT surfaces, the modular Berry connection simply sews together the orthonormal coordinate systems covering neighborhoods of HRRT surfaces. This geometric perspective on entanglement is a promising new tool for connecting the dynamics of entanglement and gravitation.

hep-th↗

arXiv2019

Probing typical black hole microstates

We investigate the possibility that the geometry dual to a typical AdS black hole microstate corresponds to the extended AdS-Schwarzschild geometry, including a region spacelike to the exterior. We argue that this region can be described by the mirror operators, a set of state-dependent operators in the dual CFT. We probe the geometry of a typical state by considering state-dependent deformations of the CFT Hamiltonian, which have an interpretation as a one-sided analogue of the Gao-Jafferis-Wall traversable wormhole protocol for typical states. We argue that the validity of the conjectured bulk geometry requires that out-of-time-order correlators of simple CFT operators on typical pure states must exhibit the same chaotic effects as thermal correlators at scrambling time. This condition is related to the question of whether the product of operators separated by scrambling time obey the Eigenstate Thermalization Hypothesis. We investigate some of these statements in the SYK model and discuss similarities with state-dependent perturbations of pure states in the SYK model previously considered by Kourkoulou and Maldacena. Finally, we discuss how the mirror operators can be used to implement an analogue of the Hayden-Preskill protocol.

hep-th↗

arXiv2018

Topology in time-reversal symmetric crystals

The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable quantum computation. Topological invariants are used to label distinct types of topological insulators. But it is not generally known how many or which invariants can exist in any given crystalline material. Using a new and efficient counting algorithm, we study the topological invariants that arise in time-reversal symmetric crystals. This results in a unified picture that explains the relations between all known topological invariants in these systems. It also predicts new topological phases and one entirely new topological invariant. We present explicitly the classification of all two-dimensional crystalline fermionic materials, and give a straightforward procedure for finding the analogous result in any three-dimensional structure. Our study represents a single, intuitive physical picture applicable to all topological invariants in real materials, with crystal symmetries.

cond-mat.str-el↗

arXiv2018

Classification of crystalline topological insulators through K-theory

Topological phases for free fermions in systems with crystal symmetry are classified by the topology of the valence band viewed as a vector bundle over the Brillouin zone. Additional symmetries, such as crystal symmetries which act non-trivially on the Brillouin zone, or time-reversal symmetry, endow the vector bundle with extra structure. These vector bundles are classified by a suitable version of K-theory. While relatively easy to define, these K-theory groups are notoriously hard to compute in explicit examples. In this paper we describe in detail how one can compute these K-theory groups starting with a decomposition of the Brillouin zone in terms of simple submanifolds on which the symmetries act nicely. The main mathematical tool is the Atiyah-Hirzebruch spectral sequence associated to such a decomposition, which will not only yield the explicit result for several crystal symmetries, but also sheds light on the origin of the topological invariants. This extends results that have appeared in the literature so far. We also describe examples in which this approach fails to directly yield a conclusive answer, and discuss various open problems and directions for future research.

cond-mat.mes-hall↗

arXiv2018

Aspects of capacity of entanglement

Many quantum information theoretic quantities are similar to and/or inspired by thermodynamic quantities, with entanglement entropy being a well-known example. In this paper, we study a less well-known example, capacity of entanglement, which is the quantum information theoretic counterpart of heat capacity. It can be defined as the second cumulant of the entanglement spectrum and can be loosely thought of as the variance in the entanglement entropy. We review the definition of capacity of entanglement and its relation to various other quantities such as fidelity susceptibility and Fisher information. We then calculate the capacity of entanglement for various quantum systems, conformal and non-conformal quantum field theories in various dimensions, and examine their holographic gravity duals. Resembling the relation between response coefficients and order parameter fluctuations in Landau-Ginzburg theories, the capacity of entanglement in field theory is related to integrated gravity fluctuations in the bulk. We address the question of measurability, in the context of proposals to measure entanglement and Rényi entropies by relating them to $U(1)$ charges fluctuating in and out of a subregion, for systems equivalent to non-interacting fermions. From our analysis, we find universal features in conformal field theories, in particular the area dependence of the capacity of entanglement appears to track that of the entanglement entropy. This relation is seen to be modified under perturbations from conformal invariance. In quenched 1+1 dimensional CFTs, we compute the rate of growth of the capacity of entanglement. The result may be used to refine the interpretation of entanglement spreading being carried by ballistic propagation of entangled quasiparticle pairs created at the quench.

hep-th↗

arXiv2018

Comments on a state-operator correspondence for the torus

We investigate the existence of a state-operator correspondence on the torus. This correspondence would relate states of the CFT Hilbert space living on a spatial torus to the path integral over compact Euclidean manifolds with operator insertions. Unlike the states on the sphere that are associated to local operators, we argue that those on the torus would more naturally be associated to line operators. We find evidence that such a correspondence cannot exist and in particular, we argue that no compact Euclidean path integral can produce the vacuum on the torus. Our arguments come solely from field theory and formulate a CFT version of the Horowitz-Myers conjecture for the AdS soliton.

hep-th↗

arXiv2018

Perfect Fluids

We develop a new theory of perfect fluids with translation and rotation symmetry, which is also applicable in the absence of any type of boost symmetry. It involves introducing a new fluid variable, the kinetic mass density, which is needed to define the most general energy-momentum tensor for perfect fluids. Our theory leads to corrections to the Euler equations for perfect fluids that might be observable in hydrodynamic fluid experiments. We also derive new expressions for the speed of sound in perfect fluids. Our theory reduces to the known perfect fluid models when boost symmetry is present. It can also be adapted to (non-relativistic) scale invariant fluids with critical exponent $z$. We show that perfect fluids cannot have Schrödinger symmetry unless $z=2$. For generic values of $z$ there can be fluids with Lifshitz symmetry, and as a concrete example, we work out in detail the thermodynamics and fluid description of an ideal gas of Lifshitz particles and compute the speed of sound for the classical and quantum Lifshitz gasses.

hep-th↗

arXiv2018

Hydrodynamic Modes of Homogeneous and Isotropic Fluids

Relativistic fluids are Lorentz invariant, and a non-relativistic limit of such fluids leads to the well-known Navier-Stokes equation. However, for fluids moving with respect to a reference system, or in critical systems with generic dynamical exponent z, the assumption of Lorentz invariance (or its non-relativistic version) does not hold. We are thus led to consider the most general fluid assuming only homogeneity and isotropy and study its hydrodynamics and transport behaviour. Remarkably, such systems have not been treated in full generality in the literature so far. Here we study these equations at the linearized level. We find new expressions for the speed of sound, corrections to the Navier-Stokes equation and determine all dissipative and non-dissipative first order transport coefficients. Dispersion relations for the sound, shear and diffusion modes are determined to second order in momenta. In the presence of a scaling symmetry with dynamical exponent z, we show that the sound attenuation constant depends on both shear viscosity and thermal conductivity.

hep-th↗

arXiv2018

Chaotic strings in AdS/CFT

Holographic theories with classical gravity duals are maximally chaotic; i.e., they saturate the universal bound on the rate of growth of chaos. It is interesting to ask whether this property is true only for leading large $N$ correlators or if it can show up elsewhere. In this Letter we consider the simplest setup to tackle this question: a Brownian particle coupled to a thermal ensemble. We find that the four-point out-of-time-order correlator that diagnoses chaos initially grows at an exponential rate that saturates the chaos bound, i.e., with a Lyapunov exponent $λ_L=2π/β$. However, the scrambling time is parametrically smaller than for plasma excitations, $t_*\simβ\log \sqrtλ$ instead of $t_*\simβ\log N^2$. Our result shows that, at least in certain cases, maximal chaos can be attained in the probe sector without the explicit need of gravitational degrees of freedom.

hep-th↗

arXiv2018

On the interior geometry of a typical black hole microstate

We argue that the region behind the horizon of a one-sided black hole can be probed by an analogue of the double-trace deformation protocol of Gao-Jafferis-Wall. This is achieved via a deformation of the CFT Hamiltonian by a term of the form ${\cal O} \widetilde{\cal O}$, where $\widetilde{\cal O}$ denote the state-dependent "mirror operators". We argue that this deformation creates negative energy shockwaves in the bulk, which allow particles inside the horizon to escape and to get directly detected in the CFT. This provides evidence for the smoothness of the horizon of black holes dual to typical states. We argue that the mirror operators allow us to perform an analogue of the Hayden-Preskill decoding protocol. Our claims rely on a technical conjecture about the chaotic behavior of out-of-time-order correlators on typical pure states at scrambling time.

hep-th↗

arXiv2017

Universality of Sparse $d>2$ Conformal Field Theory at Large $N$

We derive necessary and sufficient conditions for large $N$ conformal field theories to have a universal free energy and an extended range of validity of the higher-dimensional Cardy formula. These constraints are much tighter than in two dimensions and must be satisfied by any conformal field theory dual to Einstein gravity. We construct and analyze symmetric product orbifold theories on $\mathbb{T}^d$ and show that they only realize the necessary phase structure and extended range of validity if the seed theory is assumed to have a universal vacuum energy.

hep-th↗

arXiv2016

Precursors and BRST Symmetry

In the AdS/CFT correspondence, bulk information appears to be encoded in the CFT in a redundant way. A local bulk field corresponds to many different non-local CFT operators (precursors). We recast this ambiguity in the language of BRST symmetry, and propose that in the large $N$ limit, the difference between two precursors is a BRST exact and ghost-free term. Using the BRST formalism and working in a simple model with global symmetries, we re-derive a precursor ambiguity appearing in earlier work. Finally, we show within this model that this BRST ambiguity has the right number of parameters to explain the freedom to localize precursors within the boundary of an entanglement wedge order by order in the large $N$ expansion.

hep-th↗

arXiv2016

Topological classification of crystalline insulators through band structure combinatorics

We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure. The algorithm applies to crystals with broken time-reversal, particle-hole, and chiral symmetries in any dimension. The presented results match the mathematical structure underlying the topological classification of these crystals in terms of K-theory, and therefore elucidate this abstract mathematical framework from a simple combinatorial perspective. Using a straightforward counting procedure, we classify the allowed topological phases in any possible two-dimensional crystal in class A. We also show how the same procedure can be used to classify the allowed phases for any three-dimensional space group. Employing these classifications, we study transitions between topological phases within class A that are driven by band inversions at high symmetry points in the first Brillouin zone. This enables us to list all possible types of phase transitions within a given crystal structure, and identify whether or not they give rise to intermediate Weyl semimetallic phases.

cond-mat.mes-hall↗

arXiv2016

Entanglement, Holography and Causal Diamonds

We argue that the degrees of freedom in a d-dimensional CFT can be re-organized in an insightful way by studying observables on the moduli space of causal diamonds (or equivalently, the space of pairs of timelike separated points). This 2d-dimensional space naturally captures some of the fundamental nonlocality and causal structure inherent in the entanglement of CFT states. For any primary CFT operator, we construct an observable on this space, which is defined by smearing the associated one-point function over causal diamonds. Known examples of such quantities are the entanglement entropy of vacuum excitations and its higher spin generalizations. We show that in holographic CFTs, these observables are given by suitably defined integrals of dual bulk fields over the corresponding Ryu-Takayanagi minimal surfaces. Furthermore, we explain connections to the operator product expansion and the first law of entanglement entropy from this unifying point of view. We demonstrate that for small perturbations of the vacuum, our observables obey linear two-derivative equations of motion on the space of causal diamonds. In two dimensions, the latter is given by a product of two copies of a two-dimensional de Sitter space. For a class of universal states, we show that the entanglement entropy and its spin-three generalization obey nonlinear equations of motion with local interactions on this moduli space, which can be identified with Liouville and Toda equations, respectively. This suggests the possibility of extending the definition of our new observables beyond the linear level more generally and in such a way that they give rise to new dynamically interacting theories on the moduli space of causal diamonds. Various challenges one has to face in order to implement this idea are discussed.

hep-th↗

arXiv2016

Comments on Thermalization in 2D CFT

We revisit certain aspects of thermalization in 2D CFT. In particular, we consider similarities and differences between the time dependence of correlation functions in various states in rational and non-rational CFTs. We also consider the distinction between global and local thermalization and explain how states obtained by acting with a diffeomorphism on the ground state can appear locally thermal, and we review why the time-dependent expectation value of the energy-momentum tensor is generally a poor diagnostic of global thermalization. Since all 2D CFTs have an infinite set of commuting conserved charges, generic initial states might be expected to give rise to a generalized Gibbs ensemble rather than a pure thermal ensemble at late times. We construct the holographic dual of the generalized Gibbs ensemble and show that, to leading order, it is still described by a BTZ black hole. The extra conserved charges, while rendering $c < 1$ theories essentially integrable, therefore seem to have little effect on large-$c$ conformal field theories.

hep-th↗

arXiv2016

Holographic de Sitter Geometry from Entanglement in Conformal Field Theory

We demonstrate that for general conformal field theories (CFTs), the entanglement for small perturbations of the vacuum is organized in a novel holographic way. For spherical entangling regions in a constant time slice, perturbations in the entanglement entropy are solutions of a Klein-Gordon equation in an auxiliary de Sitter (dS) spacetime. The role of the emergent time-like direction in dS is played by the size of the entangling sphere. For CFTs with extra conserved charges, e.g., higher spin charges, we show that each charge gives rise to a separate dynamical scalar field in dS.

hep-th↗