arXiv subjects

Hyun-Sik Jeong

Publications and source records attributed to Hyun-Sik Jeong.

49 records · Page 3Linked to original sources

arXiv2021

Islands in charged linear dilaton black holes

We investigate the Page curve for a non-standard black hole which is asymptotically non-flat/AdS/dS. For this purpose, we apply the island prescription to the charged linear dilaton black holes and analyze, in detail, the entanglement entropy of Hawking radiation for both the non-extremal case and the extremal case. In the non-extremal case, we find the Page curve consistent with the unitarity principle: at early times the entanglement entropy grows linearly in time without the island and at late times it is saturated double of the Bekenstein-Hawking entropy in the presence of the island. We observe the Page time is universal for all different models studied by our method: $t_{\text{Page}}=\frac{3}{ πc}\frac{S_{\text{BH}}}{T_H}.$ For the extremal case, the island prescription provides the well defined entanglement entropy only with the island, which can not be obtained from the continuous limit of the non-extremal case. This implies that the Page curve may not be reproduced for the extremal case and further investigation is needed.

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arXiv2021

The breakdown of magneto-hydrodynamics near AdS$_2$ fixed point and energy diffusion bound

We investigate the breakdown of magneto-hydrodynamics at low temperature ($T$) with black holes whose extremal geometry is AdS$_2\times$R$^2$. The breakdown is identified by the equilibration scales ($ω_{\text{eq}}, k_{\text{eq}}$) defined as the collision point between the diffusive hydrodynamic mode and the longest-lived non-hydrodynamic mode. We show ($ω_{\text{eq}}, k_{\text{eq}}$) at low $T$ is determined by the diffusion constant $D$ and the scaling dimension $Δ(0)$ of an infra-red operator: $ω_{\text{eq}} = 2πT Δ(0), \, k_{\text{eq}}^2 = ω_{\text{eq}}/D$, where $Δ(0)=1$ in the presence of magnetic fields. For the purpose of comparison, we have analytically shown $Δ(0)=2$ for the axion model independent of the translational symmetry breaking pattern (explicit or spontaneous), which is complementary to previous numerical results. Our results support the conjectured universal upper bound of the energy diffusion $D \,\le\, ω_{\text{eq}}/k_{\text{eq}}^2 \,:=\, v_{\text{eq}}^2 \, τ_{\text{eq}}$ where $v_{\text{eq}}:= ω_{\text{eq}}/k_{\text{eq}}$ and $τ_{\text{eq}}:=ω_{\text{eq}}^{-1}$ are the velocity and the timescale associated to equilibration, implying that the breakdown of hydrodynamics sets the upper bound of the diffusion constant $D$ at low $T$.

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arXiv2021

Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field

We investigate the properties of pole-skipping of the sound channel in which the translational symmetry is broken explicitly or spontaneously. For this purpose, we analyze, in detail, not only the holographic axion model, but also the magnetically charged black holes with two methods: the near-horizon analysis and quasi-normal mode computations. We find that the pole-skipping points are related with the chaotic properties, Lyapunov exponent ($λ_L$) and butterfly velocity ($v_B$), independently of the symmetry breaking patterns. We show that the diffusion constant ($D$) is bounded by $D \,\geqslant\, v_{B}^2/λ_{L}$, where $D$ is the energy diffusion (crystal diffusion) bound for explicit (spontaneous) symmetry breaking. We confirm that the lower bound is obtained by the pole-skipping analysis in the low temperature limit.

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arXiv2021

Pole-skipping of scalar and vector fields in hyperbolic space: conformal blocks and holography

Motivated by the recent connection between pole-skipping phenomena of two point functions and four point out-of-time-order correlators (OTOCs), we study the pole structure of thermal two-point functions in $d$-dimensional conformal field theories (CFTs) in hyperbolic space. We derive the pole-skipping points of two-point functions of scalar and vector fields by three methods (one field theoretic and two holographic methods) and confirm that they agree. We show that the leading pole-skipping point of two point functions is related with the late time behavior of conformal blocks and shadow conformal blocks in four-point OTOCs.

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arXiv2020

Classifying pole-skipping points

We clarify general mathematical and physical properties of pole-skipping points. For this purpose, we analyse scalar and vector fields in hyperbolic space. This setup is chosen because it is simple enough to allow us to obtain analytical expressions for the Green's function and check everything explicitly, while it contains all the essential features of pole-skipping points. We classify pole-skipping points in three types (type-I, II, III). Type-I and Type-II are distinguished by the (limiting) behavior of the Green's function near the pole-skipping points. Type-III can arise at non-integer $iω$ values, which is due to a specific UV condition, contrary to the types I and II, which are related to a non-unique near-horizon boundary condition. We also clarify the relation between the pole-skipping structure of the Green's function and the near-horizon analysis. We point out that there are subtle cases where the near-horizon analysis alone may not be able to capture the existence and properties of the pole-skipping points.

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arXiv2020

Linear-$T$ resistivity from low to high temperature: axion-dilaton theories

The linear-$T$ resistivity is one of the hallmarks of various strange metals regardless of their microscopic details. Towards understanding this universal property, the holographic method or gauge/gravity duality has made much progress. Most holographic models have focused on the low temperature limit, where the linear-$T$ resistivity has been explained by the infrared geometry. We extend this analysis to high temperature and identify the conditions for a robust linear-$T$ resistivity up to high temperature. This extension is important because, in experiment, the linear-$T$ resistivity is observed in a large range of temperatures, up to room temperature. In the axion-dilaton theories we find that, to have a robust linear-$T$ resistivity, the strong momentum relaxation is a necessary condition, which agrees with the previous result for the Guber-Rocha model. However, it is not sufficient in the sense that, among large range of parameters giving a linear-$T$ resistivity in low temperature limit, only very limited parameters can support the linear-$T$ resistivity up to high temperature even in strong momentum relaxation. We also show that the incoherent term in the general holographic conductivity formula or the coupling between the dilaton and Maxwell term is responsible for a robust linear-$T$ resistivity up to high temperature.

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arXiv2020

Entanglement and Rényi Entropy of Multiple Intervals in $T\overline{T}$-Deformed CFT and Holography

We study the entanglement entropy (EE) and the Rényi entropy (RE) of multiple intervals in two-dimensional $T\overline{T}$-deformed conformal field theory (CFT) at finite temperature by field theoretic and holographic methods. First, by the replica method with the twist operators, we construct the general formula of the RE and EE up to the first order of a deformation parameter. By using our general formula, we show that the EE of multiple intervals for a holographic CFT is just a summation of the single interval case even with the small deformation. This is a non-trivial consequence from the field theory perspective, though it may be expected by the Ryu-Takayanagi formula in holography. However, the deformed RE of the two intervals is a summation of the single interval case only if the separations between the intervals are big enough. It can be understood by the tension of the cosmic branes dual to the RE. We also study the holographic EE for single and two intervals with an arbitrary cut-off radius (dual to the $T\overline{T}$ deformation) at any temperature. We confirm our holographic results agree with the field theory results with a small deformation and high temperature limit, as expected. For two intervals, there are two configurations for EE: disconnected ($s$-channel) and connected ($t$-channel) ones. We investigate the phase transition between them as we change parameters: as the deformation or temperature increases the phase transition is suppressed and the disconnected phase is more favored.

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arXiv2020

Reflected Entropy and Entanglement Wedge Cross Section with the First Order Correction

We study the holographic duality between the reflected entropy and the entanglement wedge cross section with the first order correction. In the field theory side, we consider the reflected entropy for $ρ_{AB}^m$, where $ρ_{AB}$ is the reduced density matrix for two intervals in the ground state. The reflected entropy in the 2d holographic conformal field theories is computed perturbatively up to the first order in $m-1$ by using the semiclassical conformal block. In the gravity side, we compute the entanglement wedge cross section in the backreacted geometry by cosmic branes with tension $T_m$ which are anchored at the AdS boundary. Comparing both results we find a perfect agreement, showing the duality works with the first order correction in $m-1$.

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arXiv2019

Holographic Spectral Functions with Momentum Relaxation

We study (fermionic) spectral functions in two holographic models, the Gubser-Rocha-linear axion model and the linear axion model, where translational symmetry is broken by axion fields linear to the boundary coordinates ($ψ_{I}=βδ_{Ii} x^{i}$). Here, $β$ corresponds to the strength of momentum relaxation. The spectral function is computed by the fermionic Green's function of the bulk Dirac equation, where a fermion mass, $m$, and a dipole coupling, $p$, are introduced as input parameters. By classifying the shape of spectral functions, we construct complete phase diagrams in ($m,p,β$) space for both models. We find that two phase diagrams are similar even though their background geometries are different. We also find that the effect of momentum relaxation on the (spectral function) phases of two models are similar even though the effect of momentum relaxation on the DC conductivities of two models are very different. We suspect that this is because holographic fermion does not back-react to geometry in our framework.

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arXiv2019

Scrambling in Hyperbolic Black Holes: shock waves and pole-skipping

We study the scrambling properties of $(d+1)$-dimensional hyperbolic black holes. Using the eikonal approximation, we calculate out-of-time-order correlators (OTOCs) for a Rindler-AdS geometry with AdS radius $\ell$, which is dual to a $d-$dimensional conformal field theory (CFT) in hyperbolic space with temperature $T = 1/(2 π\ell)$. We find agreement between our results for OTOCs and previously reported CFT calculations. For more generic hyperbolic black holes, we compute the butterfly velocity in two different ways, namely: from shock waves and from a pole-skipping analysis, finding perfect agreement between the two methods. The butterfly velocity $v_B(T)$ nicely interpolates between the Rindler-AdS result $v_B(T=\frac{1}{2π\ell})=\frac{1}{d-1}$ and the planar result $v_B(T \gg \frac{1}{\ell})=\sqrt{\frac{d}{2(d-1)}}$.

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arXiv2019

Complexity of Holographic Superconductors

We study the complexity of holographic superconductors (Einstein-Maxwell-complex scalar actions in $d+1$ dimension) by the `complexity = volume' (CV) conjecture. First, it seems that there is a universal property: the superconducting phase always has a smaller complexity than the unstable normal phase below the critical temperature, which is similar to a free energy. We investigate the temperature dependence of the complexity. In the low temperature limit, the complexity (of formation) scales as $T^α$, where $α$ is a function of the complex scalar mass $m^2$, the $U(1)$ charge $q$, and dimension $d$. In particular, for $m^2=0$, we find $α=d-1$, independent of $q$, which can be explained by the near horizon geometry of the low temperature holographic superconductor. Next, we develop a general numerical method to compute the time-dependent complexity by the CV conjecture. By this method, we compute the time-dependent complexity of holographic superconductors. In both normal and superconducting phase, the complexity increases as time goes on and the growth rate saturates to a temperature dependent constant. The higher the temperature is, the bigger the growth rate is. However, the growth rates do not violate the Lloyd's bound in all cases and saturate the Lloyd's bound in the high temperature limit at a late time.

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arXiv2018

Linear-$T$ resistivity at high temperature

The linear-$T$ resistivity is one of the characteristic and universal properties of strange metals. There have been many progress in understanding it from holographic perspective (gauge/gravity duality). In most holographic models, the linear-$T$ resistivity is explained by the property of the infrared geometry and valid at low temperature limit. On the other hand, experimentally, the linear-$T$ resistivity is observed in a large range of temperatures, up to room temperature. By using holographic models related to the Gubser-Rocha model, we investigate how much the linear-$T$ resistivity is robust at higher temperature above the superconducting phase transition temperature. We find that strong momentum relaxation plays an important role to have a robust linear-$T$ resistivity up to high temperature.

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arXiv2017

Thermal diffusivity and butterfly velocity in anisotropic Q-Lattice models

By using a holographic method we study a relation between the thermal diffusivity ($D_T$) and two quantum chaotic properties, Lyapunov time ($τ_L$) and butterfly velocity ($v_B$) in strongly correlated systems. It has been shown that $D_T/(v_B^2 τ_L)$ is universal in some holographic models as well as condensed matter systems including the Sachdev-Ye-Kitaev (SYK) models. We investigate to what extent this relation is universal in the Q-lattice models with infrared (IR) scaling geometry, focusing on the effect of spatial anisotropy. Indeed it was shown that $\mathcal{E}_i := D_{T,i}/(v_{B,i}^2 τ_L)$ ($i=x,y$) is determined only by some scaling exponents of the IR metric in the low temperature limit regardless of the matter fields and ultraviolet data. Inspired by this observation, in this work, we find the concrete expressions for $\mathcal{E}_i$ in terms of the critical dynamical exponents $z_i$ in each direction. By analyzing the IR scaling geometry we identify the allowed scaling parameter regimes, which enable us to compute the allowed range of $\mathcal{E}_i$. We find the lower bound of $\mathcal{E}_i$ is always $1/2$, which is not affected by anisotropy, contrary to the $η/s$ case. However, there may be an upper bound determined by anisotropy.

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