arXiv subjects

Xian-Hui Ge

Publications and source records attributed to Xian-Hui Ge.

At least 37 records · Page 2Linked to original sources

arXiv2025

On the Replica Problem in Supersymmetric SYK Models

We investigate the replica problem for Sachdev-Ye-Kitaev (SYK) models. First, we consider $n-$replicas of the non-supersymmetric SYK model, finding that this $n$-replica model is solvable only under specific conditions. We then introduce the $\mathcal{N}=1$ supersymmetry and utilize the superconformal symmetry to develop a ``multi-ordered trick" that covers the replica structure. By incorporating ordered off-diagonal couplings, we study the resulting thermal phase structure under higher-order interactions. The Lorentzian time dynamics is analyzed, and we plot the time evolution of the effective action. Furthermore, we investigate emergent superconformal symmetry in the low-energy limit of the replicated theory. In the superconformal limit, we propose an ordered super-Schwarzian action and derive reparameterization relations for the ordered coordinates. Corresponding constraints are derived for holographic matching to $\mathcal{N}=1$ super-Jackiw-Teitelboim(SJT) gravity. We numerically calculate the modular thermodynamics (modular entropy, the $n$-dependent relative entropy, and the entanglement capacity) using fully diagonal methods. Our result provide a framework for studying $n$-replica wormholes with supersymmetric SYK model.

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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.

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arXiv2025

Hall Angle of a Spatially Random Vector Model

Strange metals exhibit linear resistivity and anomalous Hall transport, yet a comprehensive theory that accounts for both phenomena is still lacking. Recent studies have shown SYK-like spatially random couplings between a Fermi surface and a bosonic field, either scalar or vector type, can yield linear-$T$ resistivity. In this paper, we continue the investigation on a vector coupling in the presence of a magnetic field. We compute the fermion and boson propagators, along with the self-energy and polarization functions, and determine their dependence on the magnetic field. Although the Hall angle does not exhibit the signature of strange-metal, the linear-in-temperature resistivity remains at low temperatures. Results indicate that random interactions can robustly support linear transport, though additional ingredients may be required to capture the full phenomenology of strange metals.

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arXiv2025

Replica Wormholes, Modular Entropy, and Capacity of Entanglement in JT Gravity

By employing the replica trick we study the impact of the replica parameter $n$ on the modular entropy and the capacity of entanglement in the End of the World (EoW) model and the island model, respectively. For the EoW model, we present $n$-dependent evolution curves of the modular entropy and the capacity of entanglement under both microcanonical and canonical ensembles. In particular, in the canonical ensemble, all quantities decrease as $n$ increases at late times. For the island model, we develop the replica geometry for finite $n$ and re-evaluate the modular entropy and the capacity of entanglement in a two-sided eternal Jackiw-Teitelboim black hole coupled with a thermal bath. In the case of a single island configuration, the modular entropy and capacity of entanglement closely resemble the thermal entropy and the heat capacity, respectively, yielding results analogous to those obtained in the canonical ensemble for the EoW model. The analysis of the results from these two models strongly indicates that in geometries with a greater number of $n$ copies, more connected geometries effectively purify thermal Hawking radiation. In addition, we compare these findings with statistical mechanics and provide an interpretation for the replica parameter $n$. Finally, we generalize the island formula to accommodate the finite $n$ case under this interpretation.

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arXiv2025

Linear-T Resistivity from Spatially Random Vector Coupling

Recently, Patel et al. introduced a higher dimensional version of the SYK model with random coupling in a Yukawa interaction to find the linear-$T$ resistivity. We test the universality of the mechanism by replacing the scalar field with a vector field in various dimensions. We find that it works for vector and scalar interactions, although the details are largely different. However, this mechanism for the linear-$T$ resistivity works only in $(2+1)$ dimensions and not in higher dimensions, regardless of the interaction type. Based on these results, we explore the rôle of spatial random disorder and find a simple explanation of how such random scattering converts the Fermi liquid to a strange metal by changing the self-energies of the involved bosons and fermions.

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arXiv2025

Dependence of the critical temperature and disorder in holographic superconductors on superfluid density

Recent experiments strongly indicate deep connections between transports of strange metal and high $T_c$ superconductors. For instance, it is known that the dependence of the zero-temperature phase stiffness on the critical superconducting temperature becomes linear in underdoped materials. In this paper, we investigate relation meticulously between the phase stiffness and the critical superconducting temperature for the Gubser-Rocha holographic superconductor model in the probe limit. The superfluid density (or phase stiffness) can be extracted from the low-frequency dependence of the AC conductivity. More importantly, we find linear dependence of zero-temperature superfluid density on the critical superconducting temperature, which has a similarity to a recent experiment in a film cuprate. In addition, we also provide some approximate formulas for the critical temperatures and the AC conductivity.

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arXiv2024

Holographic fermions in the Dyonic Gubser-Rocha black hole

We investigate the fermionic properties of a dyonic Gubser-Rocha model in the context of gauge/gravity duality. This model incorporates both a magnetic field and momentum relaxation. We have derived this model's scaling exponent, revealing the influence of the magnetic field and momentum relaxation on low-energy physics. As the magnetic field strength and momentum relaxation increase, the spectral function of the dual field changes significantly. Specifically, we observe variations in the scaling exponent, Fermi momentum, and dispersion relations as the magnetic field increases, highlighting the system's transition from a Fermi liquid to a non-Fermi liquid, and eventually to an insulating state. Our analysis of the magneto-scattering rate reveals that it is nearly zero in the Fermi liquid region, increases significantly in the non-Fermi liquid region, and ultimately arrives at a maximum value in the insulating state.

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arXiv2024

Thermodynamic and Real-time Dynamic Properties of Complex Sachdev-Ye-Kitaev Model

We study the complex Sachdev-Ye-Kitaev (cSYK) numerically and investigate thermodynamic behavior of cSYK model across varying chemical potentials. We discover that the cSYK model remarkably mirrors the first-order phase transition seen in the van der Waals-Maxwell system, culminating at a non-mean-field critical point with distinctively different critical exponents. We analyze in detail the similarity between the van der Waals phase transition and the cSYK model, and further explore the mechanism by which the chemical potential drives the phase transition in the system. Exact diagonalization for the cSYK model reveals the significant impact of chemical potential on energy distribution, with observable energy gaps in the gapped phase. Quantum chaos indicators, including spectral form factors, suggest more stable energy states in the neutral case. Real-time dynamics, analyzed via analytical continuation of Schwinger-Dyson equations, show rapid decay in the gapless phase and prolonged oscillation lifetimes in the gapped regime. Spectral functions imply a shift from a continuous to a discrete energy level distribution, emphasizing the critical role of chemical potential in shaping spectral properties.

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arXiv2024

Excitation Transmission through a non-Hermitian traversable wormhole

This study explores the intricate real-time dynamics of a non-Hermitian system composed of two interconnected Sachdev-Ye-Kitaev (SYK) models. A central finding reveals that an excitation initially localized in the right SYK subsystem can be efficiently transmitted to the left subsystem subsequent to the characteristic scrambling time, a phenomenon facilitated by the intrinsic non-Hermitian nature of the system. The defining hallmark of non-Hermiticity is manifest in the asymmetric conveyance of quantum states, with the non-Hermitian parameter functioning as a tunable knob that selectively amplifies or dampens propagation modes on either side. Despite this inherent directional bias in state transfer, the system sustains two distinct phases, analogously likened to black holes and wormholes.

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arXiv2024

First order phase transition in the D3-D7 model from the point of view of the fermionic spectral functions

We consider the D3-D7 model and use the spectral function of a probe fermion on D7 to analyze the first order phase transition from the black-hole embedding phase to another black-hole embedding phase in the presence of the finite density and temperature. From the fermionic spectral functions, we study the temperature dependence of the decay rate, and we observe various phenomena that support the first order phase transition including jump in it at the critical temperature that corresponds to the first order phase transition.

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arXiv2024

Thermodynamic Stability Versus Chaos Bound Violation in D-dimensional RN Black Holes: Angular Momentum Effects and Phase Transitions

We compute the Lyapunov exponents for test particles orbiting in unstable circular trajectories around D-dimensional Reissner-Nordström (RN) black holes, scrutinizing instances of the chaos bound violation. Notably, we discover that an increase in particle angular momentum exacerbates the breach of the chaos bound. Our research centrally investigates the correlation between black hole thermodynamic phase transitions and the breaking of the chaos limit. Findings suggest that the chaos bound can only be transgressed within thermodynamically stable phases of black holes. Specifically, in the four-dimensional scenario, the critical point of the thermodynamic phase transition aligns with the threshold condition that delineates the onset of chaos bound violation. These outcomes underscore a deep-rooted link between the thermodynamic stability of black holes and the constraints imposed by the chaos bound on particle dynamics.

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arXiv2024

Entanglement Entropy, Phase Transition, and Island Rule for Reissner-Nordström-AdS Black Holes

This study focuses on the examination of the island rule within the context of four-dimensional Reissner-Nordström-AdS (4D RN-AdS) black holes, illuminating the intricate relationship between the entanglement entropy and phase transitions of black holes. The entanglement entropy of 4D RN-AdS black holes follows the anticipated linear growth pattern before ultimately declining to a constant value, in accordance with the well-established Page curve. The novelty of this study lies in the examination of the influence, previously unexplored, of the first-order phase transition on the shape and evolution of the Page curve in situations involving both eternal and evaporating black holes. Despite the morphological alterations of the curve induced by the transition, the inherent unitarity of the system persists. As the evaporation progresses, the Page curve displays diverse configurations, unveiling phenomena that are novel and defies traditional expectations, thereby enriching our comprehension of the thermodynamics of black holes interlinked with quantum information.

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arXiv2024

Geometric Constraints via Page Curves: Insights from Island Rule and Quantum Focusing Conjecture

Exploring the inverse problem tied to the Page curve phenomenon and island paradigm, we investigate the geometric conditions underpinning black hole evaporation where information is preserved and islands manifest, giving rise to the characteristic Page curve. Focusing on a broad class of static black hole metrics in asymptotically Minkowski or (anti-)de Sitter spacetimes, we derive a pivotal constraint on the blacken factor $f(r)$ for which the island exists and reproduce the Page curve. Specifically, we reveal that a sufficient yet not universally necessary criterion -- manifested in the negativity of the second derivative of $f(r)$, i.e. $f^{\prime \prime} (r)<0$, in proximity to the event horizon where $r \sim r_h+ {\cal O} (G_N)$, ensures the emergence of Page curves in a manner transcending specific theoretical models. This pivotal finding, supported by the tenets of the quantum focusing conjecture.

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arXiv2024

Duality between Seiberg-Witten Theory and Black Hole Superradiance

The newly established Seiberg-Witten (SW)/Quasinormal Modes (QNM) correspondence offers an efficient analytical approach to calculate the QNM frequencies, which was only available numerically before. This is based on the fact that both sides are characterized by Heun-type equations. We find that a similar duality exists between Seiberg-Witten theory and black hole superradiance, since the latter can also be linked to confluent Heun equation after proper transformation. Then a dictionary is constructed, with the superradiance frequencies written in terms of gauge parameters. Further by instanton counting, and taking care of the boundary conditions through connection formula, the relating frequencies are obtained analytically, which show consistency with known numerical results.

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arXiv2023

Thermo-electric Transport of Dyonic Gubser-Rocha Black Holes

We study the thermo-electric transport coefficients of an extended version of the Gubser-Rocha model. After reviewing the two relaxation time model from holography and studying the effect of the magnetic field on thermo-electric transports from hydrodynamic theory, we present a new dilatonic dyonic asymptotically AdS black hole solution. Notice that S-duality plays an important role in finding the analytic solution with the magnetic field. Using the AdS/CMT dictionary, we analyze the electric and thermo-electric transport properties of the dual field theory. The resistivity exhibits T-linearity in the low-temperature regime. However, in the strong momentum relaxation and a strong magnetic field limit, the resistivitiy shows explicit deviation from the linear-in-T resistivity. The Hall angle is linear-in-T for both the low-temperature regime and the high-temperature regime for fixed momentum dissipation strength. The Nernst signal is a bell-shaped function in terms of the magnetic field even when the momentum relaxation is strong. Finally, we discuss the possibility of getting a semi-realistic strange metal description from our model.

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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.

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arXiv2023

Page Curves for Accelerating Black Holes

The island paradigm for the fine-grained entropy of Hawking radiation is applied to eternal charged accelerating black holes. In the absence of the island, the entanglement entropy grows linearly and divergent at late times, while once the island outside the event horizon is taken into account, the unitary Page curve is reproduced naturally. The impact of the charge and the acceleration is investigated at late times. For the Page time and the scrambling time, they both increase as the acceleration increases, while decreasing as the charge increases. In particular, neutral black holes have the largest Page time and scrambling time. It is worth noting that the Page time and the scrambling time are divergent in the extremal limit, which implies that islands may be related to the causal structure of spacetime.

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arXiv2023

Matching partition functions of deformed JT gravity and the cSYK model

Motivated by recent analogies between the large-$q$ cSYK model and charged black holes, we aim to find a concrete gravitation theory with a matching partition function. Our main focus is to match the thermodynamics of the $(0+1)$-dimensional cSYK model, with that of a $(1+1)$-dimensional gravitational model. We focus on a model of deformed JT gravity, characterized by some unknown dilaton potential function and unknown dilaton-to-Maxwell field coupling. By finding the general solutions, we are able to find the Lagrangian which produces the same partition function and equation of state as that of the considered SYK model. We go beyond showing that the thermodynamics overlaps, by also showing that the Lyapunov exponents, characterizing the degree of chaos, overlap close to the second order phase transition. In the low temperature rescaled regime, there remains open questions about the Lyapunov exponents, given that our analysis ignores the black hole back action which can be large in this regime.

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