We investigate quenches of holographic theories in a confined phase, where the energy injected is insufficient to reach the deconfined phase. In such quenches, thermalization is not associated with gravitational collapse and the formation of a black hole. Nevertheless, we attempt to characterize the late-time state of this scenario. We check a number of notions of thermalization that do not require horizon formation, and find no evidence for thermalization in our chosen parameters and initial states, even in the weakest sense.
We find that the post-quench behaviour of both local and nonlocal observables exhibit oscillatory behaviour rather than decaying towards equilibrium. We generally find that the response of the nonlocal observables is smoother than that of the local ones. We discuss mechanisms which generate such smoothing, as well as "beats" which appear in the time-dependence of the nonlocal operators for certain classes of quenches. When tuning the quench parameters such that the smoothing is ineffective, we are able to perform "entanglement spectroscopy", recovering the spectrum of the confined phase of the theory from the time dependence of the entanglement entropy, as well as other nonlocal observables.
Using holographic methods we investigate the behaviour of fermionic spectral functions of strongly coupled 2+1 dimensional field theories as both temperature and chemical potential are quenched.
We study non-equilibrium dynamics and quantum quenches in a recent gauge/gravity duality model for a strongly coupled system interacting with a magnetic impurity with $SU(N)$ spin. At large $N$, it is convenient to write the impurity spin as a bilinear in Abrikosov fermions. The model describes an RG flow triggered by the marginally relevant Kondo operator. There is a phase transition at a critical temperature, below which an operator condenses which involves both an electron and an Abrikosov fermion field. This corresponds to a holographic superconductor in AdS$_2$ and models the impurity scr…
We construct gravitational backgrounds dual to a family of field theories parameterized by a relevant coupling. They combine a non-trivial scalar field profile with a naked singularity. The naked singularity is necessary to preserve Lorentz invariance along the boundary directions. The singularity is however excised by introducing an infrared cutoff in the geometry. The holographic dictionary associated to the infrared boundary is developed. We implement quenches between two different values of the coupling. This requires considering time dependent boundary conditions for the scalar field both…
We consider the entanglement entropy in 2d conformal field theory in a class of excited states produced by the insertion of a heavy local operator. These include both high-energy eigenstates of the Hamiltonian and time-dependent local quenches. We compute the universal contribution from the stress tensor to the single interval Renyi entropies and entanglement entropy, and conjecture that this dominates the answer in theories with a large central charge and a sparse spectrum of low-dimension operators. The resulting entanglement entropies agree precisely with holographic calculations in three-d…
We use the holographic duality to study quantum quenches of a strongly coupled CFT that drive the theory towards a non-relativistic fixed point with Lifshitz scaling. We consider the case of a Lifshitz dynamical exponent $z$ close to unity, where the non-relativistic field theory can be understood as a specific deformation of the corresponding CFT and, hence, the standard holographic dictionary can be applied. On the gravity side this amounts to finding a dynamical bulk solution which interpolates between AdS and Lishitz spacetimes as time evolves. We show that an asymptotically Lifshitz black…
In order to holographically model quenches with a gapped final hamiltonian, we consider a gravity-scalar theory in anti-de Sitter space with an infrared hard wall. We allow a time dependent profile for the scalar field at the wall. This induces an energy exchange between bulk and wall and generates an oscillating scalar pulse. We argue that such backgrounds are the counterpart of quantum revivals in the dual field theory. We perform a qualitative comparison with the quench dynamics of the massive Schwinger model, which has been recently analyzed using tensor network techniques. Agreement is fo…
We describe the application of pseudo-spectral methods to problems of holographic thermal quenches of relevant couplings in strongly coupled gauge theories. We focus on quenches of a fermionic mass term in a strongly coupled N=4 supersymmetric Yang-Mills plasma, and the subsequent equilibration of the system. From the dual gravitational perspective, we study the gravitational collapse of a massive scalar field in asymptotically anti-de Sitter geometry with a prescribed boundary condition for its non-normalizable mode. Access to the full background geometry of the gravitational collapse allows …
We study three different types of local quenches (local operator, splitting and joining) in both the free fermion and holographic CFTs in two dimensions. We show that the computation of a quantity called entanglement density, provides a systematic method to capture essential properties of local quenches. This allows us to clearly understand the differences between the free and holographic CFTs as well as the distinctions between three local quenches. We also analyze holographic geometries of splitting/joining local quenches using the AdS/BCFT prescription. We show that they are essentially des…
We present a gravity dual of local operator quench in a two-dimensional CFT with conformal boundaries. This is given by a massive excitation in a three-dimensional AdS space with the end of the world brane (EOW brane). Due to the gravitational backreaction, the EOW brane gets deformed in a nontrivial way. We show that the energy-momentum tensor and entanglement entropy computed from the gravity dual and from the BCFT in the large $c$ limit match perfectly. Interestingly, this comparison avoids the folding of the EOW brane in an elegant way.
We study holographic models related to global quantum quenches in finite size systems. The holographic set up describes naturally a CFT, which we consider on a circle and a sphere. The enhanced symmetry of the conformal group on the circle motivates us to compare the evolution in both cases. Depending on the initial conditions, the dual geometry exhibits oscillations that we holographically interpret as revivals of the initial field theory state. On the sphere, this only happens when the energy density created by the quench is small compared to the system size. However on the circle considerab…
We discuss the behaviour of holographic entanglement entropy following a local quench in 2+1 dimensional strongly coupled CFTs. The entanglement generated by the quench propagates along an emergent light-cone, reminiscent of the Lieb-Robinson light-cone propagation of correlations in non-relativistic systems. We find the speed of propagation is bounded from below by the entanglement tsunami velocity obtained earlier for global quenches in holographic systems, and from above by the speed of light. The former is realized for sufficiently broad quenches, while the latter pertains for well localiz…
We investigate the dynamical evolution of entanglement entropy in a holographic superconductor model by quenching the source term of the dual charged scalar operator. By access to the full background geometry, the holographic entanglement entropy is calculated for a strip geometry at the AdS boundary. It is found that the entanglement entropy exhibits a robust non-monotonic behaviour in time, independent of the strength of Gaussian quench and the size of the strip: it first displays a small dip, then grows linearly, and finally saturates. In particular, the linear growth velocity of the entang…
We study the response of the chiral magnetic effect due to continuous quenches induced by time dependent electric fields within holography. Concretely, we consider a holographic model with dual chiral anomaly and compute the electric current parallel to a constant, homogeneous magnetic field and a time dependent electric field in the probe approximation. We explicitly solve the PDEs by means of pseudospectral methods in spatial and time directions and study the transition to an universal "fast" quench response. Moreover, we compute the amplitudes, i.e.,~residues of the quasi normal modes, by s…
The quantum null energy condition (QNEC) is a lower bound on the energy-momentum tensor in terms of the variation of the entanglement entropy of a sub-region along a null direction. To gain insights into quantum thermodynamics of many-body systems, we study if the QNEC restricts irreversible entropy production in quenches driven by energy-momentum inflow from an infinite memoryless bath in two-dimensional holographic theories. We find that an increase in both entropy and temperature, as implied by the Clausius inequality of classical thermodynamics, are necessary but not sufficient to not viol…
Holographic Local Operator Quenches with Conserved Momentum and Spin
The Oskar Klein Centre and Department of Physics, Stockholm University（斯德哥尔摩大学奥斯卡·克莱因中心与物理系）；Faculty of Physics, University of Warsaw（华沙大学物理学院）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Centre for High Energy Physics, Indian Institute of Science（印度科学学院高能物理中心）；International Centre for Theoretical Sciences-TIFR（TIFR国际理论科学中心）
I propose a random network model governed by a Gaussian weight corresponding to Ising link antiferromagnetism as a model for emergent quantum space-time. In this model, discrete space is fundamental, not a regularization, its spectral dimension $d_s$ is not a model input but is, rather, completely determined by the antiferromagnetic coupling constant. Perturbative terms suppressing triangles and favouring squares lead to locally Euclidean ground states that are Ricci flat "large worlds" with power-law extension. I then consider the quenched graphs of lowest energy for $d_s=2$ and $d_s=3$ and I…
In this work we extensively study the dynamics of excited states created by instantaneous local quenches at two different points, i.e., double local quenches. We focus on setups in two dimensional holographic and free Dirac fermion CFTs. We calculate the energy stress tensor and entanglement entropy for double joining and splitting local quenches. In the splitting local quenches we find an interesting oscillating behaviors. Finally, we study the energy stress tensor in double operator local quenches. In all these examples, we find that, in general, there are non-trivial interactions between th…
Entanglement Dynamics by (Non-)Unitary Local Operator Quenches in a 2D Holographic CFT
University of Chinese Academy of Sciences（中国科学院大学）；Kyoto University（京都大学）；RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所交叉理论数学科学中心(iTHEMS)）
Understanding quantum entanglement in interacting higher-dimensional conformal field theories is a challenging task, as direct analytical calculations are often impossible to perform. With holographic entanglement entropy, calculations of entanglement entropy turn into a problem of finding extremal surfaces in a curved spacetime, which we tackle with a numerical finite-element approach. In this paper, we compute the entanglement entropy between two half-spaces resulting from a local quench, triggered by a local operator insertion in a CFT$_3$. We find that the growth of entanglement entropy at…
The celebrated holographic entropy bound asserts that, within the framework of a self-consistent quantum theory of gravity, the maximal entropy (information) content of a physical system is given by one quarter of its circumscribing area: $S\leq S_{\text{max}}={\cal A}/4{\ell^2_P}$ (here $\ell_P$ is the Planck length). An intriguing possible counter-example to this fundamental entropy bound, which involves {\it homogenous} weakly self-gravitating confined thermal fields in higher-dimensional spacetimes, has been proposed almost a decade ago. Interestingly, in the present paper we shall prove t…
In my master thesis, I investigated the chiral-magnetic effect in the context of holography; I focused in especially on the impact of the chiral anomaly at transport properties and non-equilbrium behaviour in response to an holographic quench. Concretely, I considered an $U(1)_\text{A}\times U(1)_\text{V}$-Einstein-Maxwell bottom-up model consisting of two massless gauge fields, coupled by a Chern-Simons term in the fivedimensional AdS spacetime. The two gauge fields provide a time dependent electric field and a static magnetic field, parallel to it. As response of the system to quench, I inve…
We perform computer simulations of the Berkooz-Douglas (BD) matrix model, holographically dual to the D0/D4-brane intersection. We generate the fundamental condensate versus bare mass curve of the theory both holographically and from simulations of the BD model. Our studies show excellent agreement of the two approaches in the deconfined phase of the theory and significant deviations in the confined phase. We argue the discrepancy in the confined phase is explained by the embedding of the D4-brane which yields stronger $α'$ corrections to the condensate in this phase.
We use a simple holographic toy model to study global quantum quenches in strongly-coupled, hyperscaling-violating-Lifshitz quantum field theories using entanglement entropy as a probe. Generalizing our results in arxiv:1705.10324 , we show that the holographic entanglement entropy of small subsystems can be written as a simple linear response relation. We use this relation to derive a time-dependent first law of entanglement entropy. In general, this law has a time-dependent term resembling relative entropy which we propose as a good order parameter to characterize out-of-equilibrium-states i…
A family of deformed black branes is employed to examine the confinement/deconfinement phase transition in AdS/QCD. The holographic entanglement entropy (HEE) plays the role of the order parameter driving the confinement/deconfinement phase transition. The binding energy of quark-antiquark bound states and the critical length that makes a null variation of the HEE, together with the critical temperature separating the deconfined quark-gluon plasma to the confined hadronic phase, are discussed in the deformed black brane background, matching current experimental hadronic data.
In this paper we construct time-dependent solutions of three-dimensional gravity in AdS space dual to systems with boundaries (BCFTs), following the AdS/BCFT prescription. Such solutions can be discussed in the context of the dynamics of first order phase transitions, or more generally, in the description of quantum quenches. As an example, we apply the holographic model to calculate the dynamics of the entanglement entropy of a local quench corresponding to a nucleation of a Euclidean bubble. As in the known 1+1 CFT examples of local cut and glue quenches, the holographic entanglement entropy…
We construct the gravitational solution of the Witten-Sakai-Sugimoto model by introducing a magnetic field on the flavor brane. With taking into account their backreaction, we re-solve the type IIA supergravity in the presence of the magnetic field. Our calculation shows the gravitational solutions are magnetic-dependent and analytic both in the bubble (confined) and black brane (deconfined) case. We study the dual field theory at the leading order in the ratio of the number of flavors and colors, also in the Veneziano limit. Some physical properties related to the hadronic physics in an exter…
We describe holographic thermal quenches that are inhomogeneous in space. The main characteristic of the quench is to take the system far from its equilibrium configuration. Except special extreme cases, the problem has no analytic solution. Using the numerical holography methods, we study different observables that measure thermalization such as the time evolution of the apparent horizon, two-point Wightman function and entanglement entropy (EE). Having an extra nontrivial spacial direction, allows us to study this peculiar generalization since we categorize the problem based on whether we do…
The previously proposed "Complexity=Volume" or CV-duality is probed and developed in several directions. We show that the apparent lack of universality for large and small black holes is removed if the volume is measured in units of the maximal time from the horizon to the "final slice" (times Planck area). This also works for spinning black holes. We make use of the conserved "volume current", associated with a foliation of spacetime by maximal volume surfaces, whose flux measures their volume. This flux picture suggests that there is a transfer of the complexity from the UV to the IR in holo…
We employ the holographic approach to study the thermalization in the quenched strongly-coupled field theories with very general anisotropic scalings including Lifshitz and hyperscaling violating fixed points. The holographic dual is a Vaidya-like time-dependent geometry where the asymptotic metric has general anisotropic scaling isometries. We find the Ryu-Takanayagi extremal surface and use it to calculate the time-dependent entanglement entropy between a strip region with width $2R$ and its outside region. In the special case with an isotropic metric, we also explore the entanglement entrop…
We study the time evolution of single interval Renyi and entanglement entropies following local quantum quenches in two dimensional conformal field theories at finite temperature for which the locally excited states have a finite temporal width, ε. We show that, for local quenches produced by the action of a conformal primary field, the time dependence of Renyi and entanglement entropies at order ε^2 is universal. It is determined by the expectation value of the stress tensor in the replica geometry and proportional to the conformal dimension of the primary field generating the local excitatio…
We investigate the effect of a non-zero magnetic field on the chiral condensate using a holographic QCD approach. We extend the model proposed by Iatrakis, Kiritsis and Paredes in arXiv:1010.1364 that realises chiral symmetry breaking dynamically from 5d tachyon condensation. We calculate the chiral condensate, magnetisation and susceptibilities for the confined and deconfined phases. The model leads, in the probe approximation, to magnetic catalysis of chiral symmetry breaking in both confined and deconfined phases. In the chiral limit, $m_q=0$, we find that in the deconfined phase a sufficie…
