arXiv subjects

Keun-Young Kim

Publications and source records attributed to Keun-Young Kim.

At least 37 records · Page 2Linked to original sources

arXiv2025

Islands and traversable wormholes

We study information recovery in black hole evaporation using traversable wormhole protocols in AdS$_2$ Jackiw-Teitelboim gravity with matter fields coupled to an external bath. By introducing a simple non-local interaction between left and right radiation regions, we generate negative-energy shockwaves that render the wormhole traversable. We compute the resulting shifts in Kruskal coordinates, changes in the stress tensor, and backreaction effects on quantum extremal surfaces, finding a consistent decrease of the generalized entropy that aligns with the flat Page curve. Finally, we analyze the impact of negative-energy shocks on boundary two-point functions, providing a microscopic probe of island/radiation duality and discussing possible implications for experimental realizations in analog quantum-mechanical models.

hep-th↗

arXiv2025

Statistics and Complexity of Wavefunction Spreading in Quantum Dynamical Systems

We consider the statistics of the results of a measurement of the spreading operator in the Krylov basis generated by the Hamiltonian of a quantum system starting from a specified initial pure state. We first obtain the probability distribution of the results of measurements of this spreading operator at a certain instant of time, and compute the characteristic function of this distribution. We show that the moments of this characteristic function are related to the so-called generalised spread complexities, and obtain expressions for them in several cases when the Hamiltonian is an element of a Lie algebra. Furthermore, by considering a continuum limit of the Krylov basis, we show that the generalised spread complexities of higher orders have a peak in the time evolution for a random matrix Hamiltonian belonging to the Gaussian unitary ensemble. We also obtain an upper bound on the change in generalised spread complexity at an arbitrary time in terms of the operator norm of the Hamiltonian and discuss the significance of these results.

quant-ph↗

arXiv2025

Higher-Order Krylov State Complexity in Random Matrix Quenches

In quantum many-body systems, time-evolved states typically remain confined to a smaller region of the Hilbert space known as the $\textit{Krylov subspace}$. The time evolution can be mapped onto a one-dimensional problem of a particle moving on a chain, where the average position $\langle n \rangle$ defines Krylov state complexity or spread complexity. Generalized spread complexities, associated with higher-order moments $\langle n^p \rangle$ for $p>1$, provide finer insights into the dynamics. We investigate the time evolution of generalized spread complexities following a quantum quench in random matrix theory. The quench is implemented by transitioning from an initial random Hamiltonian to a post-quench Hamiltonian obtained by dividing it into four blocks and flipping the sign of the off-diagonal blocks. This setup captures universal features of chaotic quantum quenches. When the initial state is the thermofield double state of the post-quench Hamiltonian, a peak in spread complexity preceding equilibration signals level repulsion, a hallmark of quantum chaos. We examine the robustness of this peak for other initial states, such as the ground state or the thermofield double state of the pre-quench Hamiltonian. To quantify this behavior, we introduce a measure based on the peak height relative to the late-time saturation value. In the continuous limit, higher-order complexities show increased sensitivity to the peak, supported by numerical simulations for finite-size random matrices.

hep-th↗

arXiv2025

Pole-skipping in two-dimensional de Sitter spacetime and double-scaled SYK model

We develop the pole-skipping structure in de Sitter (dS) spacetime and find that their leading frequencies satisfy the relation $ω_{dS}=i2πT_{dS}(1-s)$, where $T_{dS}=1/2πL$ and $s$ denotes spin. In the two-dimensional dS spacetime, the pole-skipping points near the cosmic horizon $r=L$ for the scalar field of spin-0 and the fermionic field of spin-$\frac{1}{2}$ correspond one-to-one with those in the classical limit as $λ\rightarrow 0$ in double-scaled Sachdev-Ye-Kitaev model when the temperature is infinite (DSSYK$_\infty$). This provides a numerical correspondence between quantum gravity in the static patch of two-dimensional dS spacetime and a one-dimensional quantum system, which we consider as a realization of the DS/dS correspondence.

hep-th↗

arXiv2025

Renyi reflected entropy and entanglement wedge cross section with cosmic branes in AdS/BCFT

In this study, we calculate the $m-1$ correction to the reflected entropy for two adjacent intervals on a half-infinite line within the AdS$_3$/BCFT$_2$ framework, where $m$ is a Renyi index for a canonical purification. We utilize the doubling trick and compute the leading terms in the large central charge expansion of correlation functions in the holographic BCFT. In the corresponding AdS space with an end of the world brane, we analyze the entanglement wedge cross section, the dual counterpart of reflected entropy. This AdS/BCFT setup allows us to explore a richer set of phases in the entanglement wedge cross section. The $m-1$ correction in the holographic BCFT manifests as modifications in the entanglement wedge cross section induced by cosmic branes. For the adjacent intervals anchored to the boundary of BCFT, we show the duality between the entanglement wedge cross section with the backreaction from a cosmic brane and Renyi reflected entropy at all orders in $m-1$. Furthermore, by analyzing the entanglement wedge cross section for general adjacent intervals, we provide guidance for an $ε$-expansion of five-point functions in the holographic CFT, where $ε$ is the rescaled conformal dimension by the central charge.

hep-th↗

arXiv2025

Wedge Holographic Complexity in Karch-Randall Braneworld

We investigate holographic complexities in the context of wedge holography, focusing specifically on black string geometry in AdS$_3$. The wedge spacetime is bounded by two end-of-the-world (EOW) branes with intrinsic Dvali-Gabadadze-Porrati (DGP) gravity. In line with this codimension-two holography, there are three equivalent perspectives: bulk perspective, brane perspective, and boundary perspective. Using both the ''Complexity=Volume'' (CV) and ''Complexity=Action'' (CA) proposals, we analyze the complexity in wedge black string geometry in the tensionless limit. By treating the branes as rigid, we find the late-time growth rates of CV and CA match exactly across bulk and brane perspectives. These results are consistent with those from JT gravity, with additional contributions from the intrinsic gravity of the branes. For fluctuating branes, we find that the late-time growth rates of CV and CA match between bulk and brane perspectives at the linear order of fluctuation. The CV results exhibit $\frac{ϕ_h^2}{ϕ_0}$ corrections from fluctuations, consistent with the findings in previous work. Moreover, the CA results reveal an additional constant term in the fluctuating branes case. We provide an interpretation of this in terms of gravitational edge mode effects. The distinct corrections arising from fluctuations in the CA and CV proposals suggest that the CV proposal is more sensitive to geometric details. Furthermore, we discuss these results in relation to Lloyd's bound on complexity, their general time dependence, and the effects of fluctuations.

hep-th↗

arXiv2025

Singular Value Decomposition and Its Blind Spot for Quantum Chaos in Non-Hermitian Sachdev-Ye-Kitaev Models

The study of chaos and complexity in non-Hermitian quantum systems poses significant challenges due to the emergence of complex eigenvalues in their spectra. Recently, the singular value decomposition (SVD) method was proposed to address these challenges. In this work, we identify two critical shortcomings of the SVD approach when analyzing Krylov complexity and spectral statistics in non-Hermitian settings. First, we show that SVD fails to reproduce conventional eigenvalue statistics in the Hermitian limit for systems with non-positive definite spectra, as exemplified by a variant of the Sachdev-Ye-Kitaev (SYK) model. Second, and more fundamentally, Krylov complexity and spectral statistics derived via SVD cannot distinguish chaotic from integrable non-Hermitian dynamics, leading to results that conflict with complex spacing ratio analysis. Our findings reveal that SVD is inadequate for probing quantum chaos in non-Hermitian systems, and we advocate employing more robust methods, such as the bi-Lanczos algorithm, for future research in this direction.

hep-th↗

arXiv2025

Krylov complexity as an order parameter for quantum chaotic-integrable transitions

Krylov complexity has recently emerged as a new paradigm to characterize quantum chaos in many-body systems. However, which features of Krylov complexity are prerogative of quantum chaotic systems and how they relate to more standard probes, such as spectral statistics or out-of-time-order correlators (OTOCs), remain open questions. Recent insights have revealed that in quantum chaotic systems Krylov state complexity exhibits a distinct peak during time evolution before settling into a well-understood late-time plateau. In this work, we propose that this Krylov complexity peak (KCP) is a hallmark of quantum chaotic systems and suggest that its height could serve as an `order parameter' for quantum chaos. We demonstrate that the KCP effectively identifies chaotic-integrable transitions in two representative quantum mechanical models at both infinite and finite temperature: the mass-deformed Sachdev-Ye-Kitaev model and the sparse Sachdev-Ye-Kitaev model. Our findings align with established results from spectral statistics and OTOCs, while introducing an operator-independent diagnostic for quantum chaos, offering more `universal' insights and a deeper understanding of the general properties of quantum chaotic systems.

hep-th↗

arXiv2025

Deep learning-based holography for T-linear resistivity

We employ deep learning within holographic duality to investigate $T$-linear resistivity, a hallmark of strange metals. Utilizing Physics-Informed Neural Networks, we incorporate boundary data for $T$-linear resistivity and bulk differential equations into a loss function. This approach allows us to derive dilaton potentials in Einstein-Maxwell-Dilaton-Axion theories, capturing essential features of strange metals, such as $T$-linear resistivity and linear specific heat scaling. We also explore the impact of the resistivity slope on dilaton potentials. Regardless of slope, dilaton potentials exhibit universal exponential growth at low temperatures, driving $T$-linear resistivity and matching infrared geometric analyses. At a specific slope, our method rediscovers the Gubser-Rocha model, a well-known holographic model of strange metals. Additionally, the robustness of $T$-linear resistivity at higher temperatures correlates with the asymptotic AdS behavior of the dilaton coupling to the Maxwell term. Our findings suggest that deep learning could help uncover mechanisms in holographic condensed matter systems and advance our understanding of strange metals.

hep-th↗

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.

hep-th↗

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.

hep-th↗

arXiv2024

Krylov Complexity in Free and Interacting Scalar Field Theories with Bounded Power Spectrum

We study a notion of operator growth known as Krylov complexity in free and interacting massive scalar quantum field theories in $d$-dimensions at finite temperature. We consider the effects of mass, one-loop self-energy due to perturbative interactions, and finite ultraviolet cutoffs in continuous momentum space. These deformations change the behavior of Lanczos coefficients and Krylov complexity and induce effects such as the "staggering" of the former into two families, a decrease in the exponential growth rate of the latter, and transitions in their asymptotic behavior. We also discuss the relation between the existence of a mass gap and the property of staggering, and the relation between our ultraviolet cutoffs in continuous theories and lattice theories.

hep-th↗

arXiv2024

Traversable wormholes via a double trace deformation involving $U(1)$ conserved current operators

We study the effects of conservation laws on wormholes that are made traversable by a double trace deformation. After coupling the two asymptotic boundaries of a maximally extended $(d+1)$ dimensional black brane geometry with $U(1)$ conserved current operators, we find that the quantum matter stress-energy tensor of the corresponding bulk gauge fields in the hydrodynamic limit violates the averaged null energy condition (ANEC), rendering the wormhole traversable. Applying our results to axionic two-sided black hole solutions, we discuss how the wormhole opening depends on the charge diffusion constant, how this affects the amount of information that can be sent through the wormhole, and possible implications for many-body quantum teleportation protocols involving conserved current operators.

hep-th↗

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 $β\neq 0$.

hep-th↗

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.

hep-th↗

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.

hep-th↗

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.

cond-mat.str-el↗

arXiv2023

Pole-skipping points in 2D gravity and SYK model

We represent the first investigation of pole-skipping on both the gravity and field theory sides. In contrast to the higher dimensional models, there is no momentum degree of freedom in $(1+1)-$dimensional bulk theory. Thus, we then consider a scalar field mass as our degree of freedom for the pole-skipping phenomenon instead of momentum. The pole-skipping frequencies of the scalar field in 2D gravity are the same as higher dimensional cases: $ω=-i2πTn$ for positive integers $n$. At each of these frequencies, there is a corresponding pole-skipping mass, so the pole-skipping points exist in $(ω,m)$ space. We also compute the pole-skipping points of the SYK model in $(ω, h)$ space where $h$ is the dimension of the bilinear primary operator. We find that there is a one-to-one correspondence of the pole-skipping points between the JT gravity and the SYK model. To obtain the pole-skipping points, we need to consider the parameter $ε$ related to the chemical potential on the horizon of charged JT gravity and the particle-hole asymmetric parameter $\mathcal{E}$ of the complex SYK model as shift parameters. This highlights the $ε-\mathcal{E}$ correspondence in relation to pole-skipping phenomenon.

hep-th↗