arXiv subjects

Hyun-Sik Jeong

Publications and source records attributed to Hyun-Sik Jeong.

At least 37 records · Page 2Linked to original sources

arXiv2024

Holographic reconstruction of black hole spacetime: machine learning and entanglement entropy

We investigate the bulk reconstruction of AdS black hole spacetime emergent from quantum entanglement within a machine learning framework. Utilizing neural ordinary differential equations alongside Monte-Carlo integration, we develop a method tailored for continuous training functions to extract the general isotropic bulk metric from entanglement entropy data. To validate our approach, we first apply our machine learning algorithm to holographic entanglement entropy data derived from the Gubser-Rocha and superconductor models, which serve as representative models of strongly coupled matters in holography. Our algorithm successfully extracts the corresponding bulk metrics from these data. Additionally, we extend our methodology to many-body systems by employing entanglement entropy data from a fermionic tight-binding chain at half filling, exemplifying critical one-dimensional systems, and derive the associated bulk metric. We find that the metrics for a tight-binding chain and the Gubser-Rocha model are similar. We speculate this similarity is due to the metallic property of these models.

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arXiv2024

Kasner interiors from analytic hairy black holes

We conduct an exhaustive study of the interior geometry of a family of asymptotically AdS$_{d+1}$ hairy black holes in an analytically controllable setup. The black holes are exact solutions to an Einstein-Maxwell-Dilaton theory and include the well-known Gubser-Rocha model. After reviewing the setup, we scrutinize the geometry beyond the horizon, finding that these backgrounds can exhibit timelike or Kasner singularities. We generalize the no inner-horizon theorem for hairy black holes to accommodate these findings. We then consider observables sensitive to the geometry behind the horizon, such as Complexity = Anything and the thermal $a$-function. In the Kasner case, we propose a new variant of complexity that characterizes the late-time rate by the Kasner exponents, extending previous work by Jørstad, Myers and Ruan. Additionally, we elucidate the power-law behavior of the thermal $a$-function near the singularity, directly relating it to the Kasner exponents. Finally, we introduce axion-like fields in the Gubser-Rocha model to study the impact of translational symmetry breaking on the black hole interior. We show that Kasner singularities occur for both explicit and spontaneous symmetry breaking, with the Kasner exponents depending on the strength of broken translations only in the latter case.

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arXiv2024

Krylov complexity of density matrix operators

Quantifying complexity in quantum systems has witnessed a surge of interest in recent years, with Krylov-based measures such as Krylov complexity ($C_K$) and Spread complexity ($C_S$) gaining prominence. In this study, we investigate their interplay by considering the complexity of states represented by density matrix operators. After setting up the problem, we analyze a handful of analytical and numerical examples spanning generic two-dimensional Hilbert spaces, qubit states, quantum harmonic oscillators, and random matrix theories, uncovering insightful relationships. For generic pure states, our analysis reveals two key findings: (I) a correspondence between moment-generating functions (of Lanczos coefficients) and survival amplitudes, and (II) an early-time equivalence between $C_K$ and $2C_S$. Furthermore, for maximally entangled pure states, we find that the moment-generating function of $C_K$ becomes the Spectral Form Factor and, at late-times, $C_K$ is simply related to $NC_S$ for $N\geq2$ within the $N$-dimensional Hilbert space. Notably, we confirm that $C_K = 2C_S$ holds across all times when $N=2$. Through the lens of random matrix theories, we also discuss deviations between complexities at intermediate times and highlight subtleties in the averaging approach at the level of the survival amplitude.

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arXiv2024

Spread and Spectral Complexity in Quantum Spin Chains: from Integrability to Chaos

We explore spread and spectral complexity in quantum systems that exhibit a transition from integrability to chaos, namely the mixed-field Ising model and the next-to-nearest-neighbor deformation of the Heisenberg XXZ spin chain. We corroborate the observation that the presence of a peak in spread complexity before its saturation, is a characteristic feature in chaotic systems. We find that, in general, the saturation value of spread complexity post-peak depends not only on the spectral statistics of the Hamiltonian, but also on the specific state. However, there appears to be a maximal universal bound determined by the symmetries and dimension of the Hamiltonian, which is realized by the thermofield double state (TFD) at infinite temperature. We also find that the time scales at which the spread complexity and spectral form factor change their behaviour agree with each other and are independent of the chaotic properties of the systems. In the case of spectral complexity, we identify that the key factor determining its saturation value and timescale in chaotic systems is given by minimum energy difference in the theory's spectrum. This explains observations made in the literature regarding its earlier saturation in chaotic systems compared to their integrable counterparts. We conclude by discussing the properties of the TFD which, we conjecture, make it suitable for probing signatures of chaos in quantum many-body systems.

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arXiv2024

Spread complexity in saddle-dominated scrambling

Recently, the concept of spread complexity, Krylov complexity for states, has been introduced as a measure of the complexity and chaoticity of quantum systems. In this paper, we study the spread complexity of the thermofield double state within \emph{integrable} systems that exhibit saddle-dominated scrambling. Specifically, we focus on the Lipkin-Meshkov-Glick model and the inverted harmonic oscillator as representative examples of quantum mechanical systems featuring saddle-dominated scrambling. Applying the Lanczos algorithm, our numerical investigation reveals that the spread complexity in these systems exhibits features reminiscent of \emph{chaotic} systems, displaying a distinctive ramp-peak-slope-plateau pattern. Our results indicate that, although spread complexity serves as a valuable probe, accurately diagnosing true quantum chaos generally necessitates additional physical input. We also explore the relationship between spread complexity, the spectral form factor, and the transition probability within the Krylov space. We provide analytical confirmation of our numerical results, validating the Ehrenfest theorem of complexity and identifying a distinct quadratic behavior in the early-time regime of spread complexity.

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arXiv2024

On pole-skipping with gauge-invariant variables in holographic axion theories

We study the pole-skipping phenomenon within holographic axion theories, a common framework for studying strongly coupled systems with chemical potential ($μ$) and momentum relaxation ($β$). Considering the backreaction characterized by $μ$ and $β$, we encounter coupled equations of motion for the metric, gauge, and axion field, which are classified into spin-0, spin-1, and spin-2 channels. Employing gauge-invariant variables, we systematically address these equations and explore pole-skipping points within each sector using the near-horizon method. Our analysis reveals two classes of pole-skipping points: regular and singular pole-skipping points in which the latter is identified when standard linear differential equations exhibit singularity. Notably, pole-skipping points in the lower-half plane are regular, while those elsewhere are singular. This suggests that the pole-skipping point in the spin-0 channel, associated with quantum chaos, corresponds to a singular pole-skipping point. Additionally, we observe that the pole-skipping momentum, if purely real or imaginary for $μ=β=0$, retains this characteristic for $μ\neq0$ and $β\neq 0$.

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arXiv2024

Deep learning bulk spacetime from boundary optical conductivity

We employ a deep learning method to deduce the \textit{bulk} spacetime from \textit{boundary} optical conductivity. We apply the neural ordinary differential equation technique, tailored for continuous functions such as the metric, to the typical class of holographic condensed matter models featuring broken translations: linear-axion models. We successfully extract the bulk metric from the boundary holographic optical conductivity. Furthermore, as an example for real material, we use experimental optical conductivity of $\text{UPd}_2\text{Al}_3$, a representative of heavy fermion metals in strongly correlated electron systems, and construct the corresponding bulk metric. To our knowledge, our work is the first illustration of deep learning bulk spacetime from \textit{boundary} holographic or experimental conductivity data.

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arXiv2023

Entanglement entropy analysis of dyonic black holes using doubly holographic theory

We investigate the entanglement between the eternal black hole and Hawking radiation. For this purpose, we utilize the doubly holographic theories and study the entanglement entropy of the radiation to find the Page curve consistent with the unitarity principle. Doubly holographic theories introduce two types of boundaries in the AdS bulk, namely the usual AdS boundary and the Planck brane. In such a setup, we calculate the entanglement entropy by examining two extremal surfaces: the Hartman-Maldacena (HM) surface and the island surface. The latter surface emerges when the island appears on the Planck brane. In this paper, we provide a detailed analysis of dyonic black holes with regard to the Page curve in the context of the doubly holographic setup. To begin with, we ascertain that the pertinent topological terms must be included in the Planck brane to describe the systems at finite density and magnetic field. Furthermore, we also develop a general numerical method to compute the time-dependent HM surface and achieve excellent agreement between the numerical results and analytical expressions. Utilizing numerical methodology, we find that the entanglement entropy of dyonic black holes exhibits unitary evolution over time, wherein it grows in early time and reaches saturation after the Page time. The initial growth can be explained by the HM surface, while the saturation is attributed to the island surface. In addition, using the holographic entanglement density, we also show that, for the first time, the saturated value of the entanglement entropy is twice the Bekenstein-Hawking entropy with the tensionless brane in double holography.

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arXiv2023

Inability of linear axion holographic Gubser-Rocha model to capture all the transport anomalies of strange metals

In the last decade, motivated by the concept of Planckian relaxation and the possible existence of a quantum critical point in cuprate materials, holographic techniques have been extensively used to tackle the problem of strange metals and high-$T_c$ superconductors. Among the various setups, the linear axion Gubser-Rocha model has often been considered as a promising holographic model for strange metals since endowed with the famous linear in $T$ resistivity property. As fiercely advocated by Phil Anderson, beyond $T$-linear resistivity, there are several additional anomalies unique to the strange metal phase, as for example a Fermi liquid like Hall angle -- the famous problem of the two relaxation scales. In this short note, we show that the linear axion holographic Gubser-Rocha model, which presents a single momentum relaxation time, fails in this respect and therefore is not able to capture the transport phenomenology of strange metals. We prove our statement by means of a direct numerical computation, a previously demonstrated scaling analysis and also a hydrodynamic argument. Finally, we conclude with an optimistic discussion on the possible improvements and generalizations which could lead to a holographic model for strange metals in all their glory.

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arXiv2023

Pole-Skipping in Rotating BTZ Black Holes

Motivated by the connection between pole-skipping phenomena of two point functions and four point out-of-time-order correlators, we study the pole-skipping phenomena for rotating BTZ black holes. In particular, we investigate the effect of rotations on the pole-skipping point for various fields with spin $s = 1/2, 1, 2/3$, extending the previous research for $s=0, 2$. We derive an analytic full tower of the pole-skipping points of fermionic ($s=1/2$) and vector ($s=1$) fields by the exact holographic Green's functions. For the \textit{non-extremal} black hole, the leading pole-skipping frequency is $ω_{\text{leading}}=2πi T_h {(s-1+νΩ)}/{(1-Ω^2)}$ where $T_h$ is the temperature, $Ω$ the rotation, and $ν:=(Δ_+ - Δ_-)/2$, the difference of conformal dimensions ($Δ_{\pm}$). These are confirmed by another independent method: the near-horizon analysis. For the \textit{extremal} black hole, we find that the leading pole-skipping frequency can occur at $ω_{\text{leading}}^{\text{extremal}}=-2πi T_R {(s+1)}$ only when $ν= s+1$, where $T_R$ is the temperature of the right moving mode. It is non-trivial because it cannot be achieved by simply taking the extreme limit ($T_h\rightarrow 0\,, Ω\rightarrow 1$) of the non-extremal black hole result.

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arXiv2023

Spectral and Krylov Complexity in Billiard Systems

In this work, we investigate spectral complexity and Krylov complexity in quantum billiard systems at finite temperature. We study both circle and stadium billiards as paradigmatic examples of integrable and non-integrable quantum-mechanical systems, respectively. We show that the saturation value and time scale of spectral complexity may be used to probe the non-integrability of the system since we find that when computed for the circle billiard, it saturates at a later time scale compared to the stadium billiards. This observation is verified for different temperatures. Furthermore, we study the Krylov complexity of the position operator and its associated Lanczos coefficients at finite temperature using the Wightman inner product. We find that the growth rate of the Lanczos coefficients saturates the conjectured universal bound at low temperatures. Additionally, we also find that even a subset of the Lanczos coefficients can potentially serve as an indicator of integrability, as they demonstrate erratic behavior specifically in the circle billiard case, in contrast to the stadium billiard. Finally, we also study Krylov entropy and verify its early-time logarithmic relation with Krylov complexity in both types of billiard systems.

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arXiv2023

Collective dynamics and the Anderson-Higgs mechanism in a bona fide holographic superconductor

The holographic superconductor is one of the most popular models in the context of applied holography. Despite what its name suggests, it does not describe a superconductor. On the contrary, the low temperature phase of its dual field theory is a superfluid with a spontaneously broken U(1) global symmetry. As already observed in the previous literature, a bona fide holographic superconductor can be constructed using mixed boundary conditions for the bulk gauge field. By exploiting this prescription, we study the near-equilibrium collective dynamics in the Higgs phase and reveal the characteristic features of the Anderson-Higgs mechanism. We show that second sound disappears from the spectrum and the gauge field acquires a finite energy gap of the order of the plasma frequency. We observe an overdamped to underdamped crossover for the Higgs mode which acquires a finite energy gap below $\approx T_c/2$, with $T_c$ the superconducting critical temperature. Interestingly, the energy gap of the Higgs mode at low temperature is significantly smaller than $2Δ$, with $Δ$ the superconducting energy gap. Finally, we interpret our results using Ginzburg-Landau theory and we confirm the validity of previously derived perturbative analytic expressions.

hep-th↗

arXiv2022

Holography and magnetohydrodynamics with dynamical gauge fields

Within the framework of holography, the Einstein-Maxwell action with Dirichlet boundary conditions corresponds to a dual conformal field theory in presence of an external gauge field. Nevertheless, in many real-world applications, e.g., magnetohydrodynamics, plasma physics, superconductors, etc. dynamical gauge fields and Coulomb interactions are fundamental. In this work, we consider bottom-up holographic models at finite magnetic field and (free) charge density in presence of dynamical boundary gauge fields which are introduced using mixed boundary conditions. We numerically study the spectrum of the lowest quasi-normal modes and successfully compare the obtained results to magnetohydrodynamics theory in $2+1$ dimensions. Surprisingly, as far as the electromagnetic coupling is small enough, we find perfect agreement even in the large magnetic field limit. Our results prove that a holographic description of magnetohydrodynamics does not necessarily need higher-form bulk fields but can be consistently derived using mixed boundary conditions for standard gauge fields.

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arXiv2022

Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy

We study the $(d+2)$-dimensional Hyperscaling Violating (HV) geometries in the presence of both a finite temperature $T$ and a UV cutoff $r_c$. This gravitational system is conjectured to be dual to $T\bar{T}$ like deformed HV QFTs. We consider the representative quantum entanglement quantity in holography, i.e. the entanglement entropy $S(A)$, and perform a complete analysis in all possible parameter ranges of the hyperscaling violation exponent $θ$ and the critical dynamical exponent $z$ to study the effect of the temperature and the cutoff. We find that the temperature has a universal effect independent of the parameters: it enhances $S(A)$ in the small cutoff limit, while it is irrelevant in the large cutoff limit. For the cutoff effect, we find that the cutoff monotonically suppresses $S(A)$ where its behavior depends on the parameter range. As an application of the finite temperature analysis, we study the first law of entanglement entropy, $S_{T}-S_{T=0}\sim\ell^λ$, in the small subsystem size $\ell$ limit. We find that $λ$ interpolates between $λ=1+z$ in the small cutoff and $λ=3$ in the large cutoff, independent of the parameter range. We also provide the analytic holographic result at $z=d-θ$ and discuss its possibility of comparison with the field theoretic result.

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arXiv2022

Holographic entanglement density for spontaneous symmetry breaking

We investigate the properties of the holographic entanglement entropy of the systems in which the $U(1)$ or the translational symmetry is broken \textit{spontaneously}. For this purpose, we define the entanglement density of the strip-subsystems and examine both the first law of entanglement entropy (FLEE) and the area theorem. We classify the conditions that FLEE and/or the area theorem obey and show that such a classification may be useful for characterizing the systems. We also find universalities from both FLEE and the area theorem. In the spontaneous symmetry breaking case, FLEE is always obeyed regardless of the type of symmetry: $U(1)$ or translation. For the translational symmetry, the area theorem is always violated when the symmetry is weakly broken, independent of the symmetry breaking patterns (explicit or spontaneous). We also argue that the $\log$ contribution of the entanglement entropy from the Goldstone mode may not appear in the strongly coupled systems.

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arXiv2022

Quasi-normal modes of dyonic black holes and magneto-hydrodynamics

We revisit the magneto-hydrodynamics in (2+1) dimensions and confirm that it is consistent with the quasi-normal modes of the (3+1) dimensional dyonic black holes in the most general set-up with finite density, magnetic field and wave vector. We investigate all possible modes (sound, shear, diffusion, cyclotron etc.) and their interplay. For the magneto-hydrodynamics we perform a complete and detailed analysis correcting some prefactors in the literature, which is important for the comparison with quasi-normal modes. For the quasi-normal mode computations in holography we identify the independent fluctuation variables of the dyonic black holes, which is nontrivial at finite density and magnetic field. As an application of the quasi-normal modes of the dyonic black holes we investigate a transport property, the diffusion constant. We find that the diffusion constant at finite density and magnetic field saturates the lower bound at low temperature. We show that this bound can be understood from the pole-skipping point.

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arXiv2021

Homes' law in holographic superconductor with linear-$T$ resistivity

Homes' law, $ρ_{s} = C \, σ_{DC} \, T_{c}$, is a universal relation of superconductors between the superfluid density $ρ_{s}$ at zero temperature, the critical temperature $T_{c}$ and the electric DC conductivity $σ_{DC}$ at $T_c$. Experimentally, Homes' law is observed in high $T_c$ superconductors with linear-$T$ resistivity in the normal phase, giving a material independent universal constant $C$. By using holographic models related to the Gubser-Rocha model, we investigate how Homes' law can be realized together with linear-$T$ resistivity in the presence of momentum relaxation. We find that strong momentum relaxation plays an important role to exhibit Homes' law with linear-$T$ resistivity.

hep-th↗

arXiv2021

Upper bound of the charge diffusion constant in holography

We investigate the upper bound of charge diffusion constant in holography. For this purpose, we apply the conjectured upper bound proposal related to the equilibration scales ($ω_{\text{eq}}, k_{\text{eq}}$) to the Einstein-Maxwell-Axion model. ($ω_{\text{eq}}, k_{\text{eq}}$) is defined as the collision point between the diffusive hydrodynamic mode and the first non-hydrodynamic mode, giving rise to the upper bound of the diffusion constant $D$ at low temperature $T$ as $D = ω_{\text{eq}}/k_{\text{eq}}^2$. We show that the upper bound proposal also works for the charge diffusion and ($ω_{\text{eq}}, k_{\text{eq}}$), at low $T$, is determined by $D$ and the scaling dimension $Δ(0)$ of an infra-red operator as $(ω_{\text{eq}}, \, k_{\text{eq}}^2) \,=\, (2 πT Δ(0) \,, ω_{\text{eq}}/D)$, as for other diffusion constants. However, for the charge diffusion, we find that the collision occurs at real $k_{\text{eq}}$, while it is complex for other diffusions. In order to examine the universality of the conjectured upper bound, we also introduce a higher derivative coupling to the Einstein-Maxwell-Axion model. This coupling is particularly interesting since it leads to the violation of the \textit{lower} bound of the charge diffusion constant so the correction may also have effects on the \textit{upper} bound of the charge diffusion. We find that the higher derivative coupling does not affect the upper bound so that the conjectured upper bound would not be easily violated.

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