arXiv subjects

Wung-Hong Huang

Publications and source records attributed to Wung-Hong Huang.

At least 19 recordsLinked to original sources

arXiv2026

OTOC and Quamtum Chaos of Interacting Scalar Fields

Discretizing the $λϕ^4$ scalar field theory on a lattice yields a system of coupled anharmonic oscillators with quadratic and quartic potentials. We begin by analyzing the two coupled oscillators in the second quantization method to derive several analytic relations to the second-order perturbation, which are then employed to numerically calculate the thermal out-of-time-order correlator (OTOC), $C_T(t)$. We find that the function $C_T(t)$ exhibits exponential growth over a long time window in the early stages, with Lyapunov exponent $λ\sim T^{1/4}$, which diagnoses quantum chaos. We furthermore investigate the quantum chaos properties in a closed chain of N coupled anharmonic oscillators, which relates to the 1+1 dimensional interacting quantum scalar field theory. The results reveal an interesting property that the signatures of quantum chaos appear at low perturbative orders in the OTOC.

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arXiv2025

Third-Order Perturbative OTOC of the Harmonic Oscillator with Quartic Interaction and Quantum Chaos

We calculate the third-order out-of-time-order correlator (OTOC) of a simple harmonic oscillator with an additional quartic interaction using the second quantization method. We obtain analytic relations for the spectrum, Fock space states, and matrix elements of the coordinate, which are then used to numerically evaluate the OTOC. We observe that after the scrambling, the OTOC becomes a fluctuation around a saturation point at later times, which is associated with quantum chaotic behavior in systems that exhibit chaos. We analyze the early-time properties of the OTOC and find that in systems with sufficiently strong quartic interactions, an exponential growth curve fitting over a long time window clearly emerges in the third-order perturbation

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arXiv2023

Second-order Perturbative OTOC of Anharmonic Oscillators

The out-of-time-order correlator (OTOC) of simple harmonic oscillator with extra anharmonic (quartic) interaction are calculated by the second quantization method. We obtain the analytic formulas of spectrum, Fock space states and matrix elements of coordinate to the second order of anharmonic interaction. These relations clearly reveal the property that the correction of the interaction is proportional to the quantum number of the energy level, and shows the enhancement for some physical quantities. The analytic results explicitly show that the OTOC is raising in the quadratic power law at early times. Then, we use the formulas to do numerical summation to calculate the OTOC, which shows that, at late times, while the first-order perturbative OTOC is oscillating as that in a simple harmonic oscillator, the second-order perturbative OTOC saturates to a constant value. We compare it with $2\langle x^2\rangle_T\langle p^2\rangle_T$, which is associated with quantum chaotic behavior in systems that exhibit chaos, and discuss the validity of the second-order perturbation.

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arXiv2023

Tri-Scalar CFT and Holographic Bi-Fishchain Model

Bi-scalar CFT from $γ$ deformed $\cal N$=4 SYM describes the fishnet theory which is integrable in the planar limit. The holographic dual of the planar model is the fishchain model. The derivation of the weak-strong duality from the first principle was presented in a recent paper (The Holographic Fishchain arXiv:1903.10508). In this note we extend the investigation to the tri-scalar CFT which raises from the large twist limit of ABJM theory. We show that it becomes tri-scalar fishnet theory in planar limit and the dual theory is the holographic bi-fishchain model.

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arXiv2023

Perturbative OTOC and Quantum Chaos in Harmonic Oscillators : Second Quantization Method

In this paper, the out-of-time-order correlators (OTOC) in quantum harmonic oscillators are calculated analytically by second quantization method in perturbative approximation. We consider the coupled harmonic oscillators and anharmonic (quartic) oscillators. The analytic formulas of microcanonical OTOC in the leading order of interaction are obtained. From these results we clearly see that the interactions can enhance the correlation to very large values over time and is proportional to the energy level. The growth of OTOC signatures the quantum chaos therein. The microcanonical OTOC which is an increasing oscillation becomes a simple increasing function in thermal OTOC after sum over all energy level, as different level oscillates with different frequency. The property that, at late time stage OTOC saturates to a constant value, however, does not show in the first-order perturbation studied in this paper.

hep-th↗

arXiv2022

Complexity of Bose-Hubbard Model : Quantum Phase Transition

The operator approach is applied to investigate the complexity of Bose-Hubbard model. We present a systematic method to expand the quantum complexity in series of coupling constant. We first study 2-sites system. For the ground state we can find the exact value of complexity which is the summation of all order. The complexity is divergent at critical value of coupling constant that indicates the quantum phase transition at this point. We then generalize the method to the N-sites closed chain and any dimensional system. The found properties are similar to those in 2-sites system. We also study the excited state and present the general formulas of Bose-Hubbard model complexity, which shows a similar form as that in $λϕ^4$ theory studied in our previous paper.

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arXiv2021

Perturbative Complexity of Interacting Theory

We present a systematic method to expand the quantum complexity of interacting theory in series of coupling constant. The complexity is evaluated by the operator approach in which the transformation matrix between the second quantization operators of reference state and the target state defines the quantum gate. We start with two coupled oscillators and perturbatively evaluate the geodesic length of the associated group manifold of gate matrix. Next, we generalize the analysis to $N$ coupled oscillators which describes the lattice $λϕ^4$ theory. Especially, we introduce simple diagrams to represent the perturbative series and construct simple rules to efficiently calculate the complexity. General formulae are obtained for the higher-order complexity of excited states. We present several diagrams to illuminate the properties of complexity and show that the interaction correction to complexity may be positive or negative depending on the magnitude of reference-state frequency.

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arXiv2019

Operator Approach to Complexity : Excited States

We evaluate the complexity of the free scalar field by the operator approach in which the transformation matrix between the second quantization operators of reference state and target state is regarded as the quantum gate. We first examine the system in which the reference state is two non-interacting oscillators with same frequency $ω_0$ while the target state is two interacting oscillators with frequency $\tilde ω_1$ and $\tilde ω_2$. We calculate the geodesic length on the associated group manifold of gate matrix and reproduce the known value of ground-state complexity. Next, we study the complexity in the excited states. Although the gate matrix is very large we can transform it to a diagonal matrix and obtain the associated complexity. We explicitly calculate the complexity in several excited states and prove that the square of geodesic length in the general state $|{\rm n,m}\rangle$ is $D_{\rm (n,m)}^2={\rm (n+1)}\left(\ln {\sqrt{\tilde ω_1\over ω_0}}\,\right)^2 +{\rm (m+1)}\left(\ln {\sqrt{\tilde ω_2\over ω_0}}\,\right)^2$. The results are extended to the N couple harmonic oscillators which correspond to the lattice version of free scalar field.

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arXiv2018

Entanglement Entropy of Compactified Branes and Phase Transition

We first calculate the holographic entanglement entropy of M5 branes on a circle and see that it has phase transition during decreasing the compactified radius. In particular, it is shown that the entanglement entropy scales as $N^3$. Next, we investigate the holographic entanglement entropy of D0+D4 system on a circle and see that it scales as $N^2$ at low energy, likes as a gauge theory with instantons. However, at high energy it transforms to a phase which scales as $N^3$, like as M5 branes system. We also present the general form of holographic entanglement entropy of Dp, ${\rm D_p+D_{p+4}}$ and M-branes on a circle and see some simple relations between them. Finally, we present an analytic method to prove that they all have phase transition from connected to disconnected surface during increasing the line segment of length $\ell$ which dividing the space.

hep-th↗

arXiv2018

Butterfly Velocity in Quadratic Gravity

We present a systematic procedure of finding the shock wave equation in anisotropic spacetime of quadratic gravity with Lagrangian ${\cal L}=R+ Λ+αR_{μνσρ}R^{μνσρ}+βR_{μν}R^{μν}+γR^2+{\cal L}_{\rm matter}$. The general formula of the butterfly velocity is derived. We show that the shock wave equation in the planar, spherical or hyperbolic black hole spacetime of Einstein-Gauss-Bonnet gravity is the same as that in Einstein gravity if space is isotropic. We consider the modified AdS spacetime deformed by the leading correction of the quadratic curvatures and find that the fourth order derivative shock wave equation leads to two butterfly velocities if $4α+β<0$. We also show that the butterfly velocity in a D=4 planar black hole is not corrected by the quadratic gravity if $ 4α+β=0$, which includes the $ R^2$ gravity. In general, the correction of butterfly velocity by the quadratic gravity may be positive or negative, depends on the values of $α$, $β$, $γ$ and temperature. We also investigate the butterfly velocity in the Gauss-Bonnet massive gravity.

hep-th↗

arXiv2018

Holographic Butterfly Velocities in Brane Geometry and Einstein-Gauss-Bonnet Gravity with Matters

In the first part of the paper we generalize the butterfly velocity formula to anisotropic spacetime. We apply the formula to evaluate the butterfly velocities in M-branes, D-branes and strings backgrounds. We show that the butterfly velocities in M2-branes, M5-branes and the intersection M2$\bot$M5 equal to those in fundamental strings, D4-branes and the intersection F1$\bot$D4 backgrounds, respectively. These observations lead us to conjecture that the butterfly velocity is generally invariant under a double-dimensional reduction. In the second part of the paper, we study the butterfly velocity for Einstein-Gauss-Bonnet gravity with arbitrary matter fields. A general formula is obtained. We use this formula to compute the butterfly velocities in different backgrounds and discuss the associated properties.

hep-th↗

arXiv2017

Butterfly Effect and Holographic Mutual Information under External Field and Spatial Noncommutativity

We apply the transformation of mixing azimuthal and internal coordinate or mixing time and internal coordinate to a stack of N black M-branes to find the Melvin spacetime of a stack of N black D-branes with magnetic or electric flux in string theory, after the Kaluza-Klein reduction. We slightly extend previous formulas to investigate the external magnetic and electric effects on the butterfly effect and holographic mutual information. It shows that the Melvin fields do not modify the scrambling time and will enhance the mutual information. In addition, we also T-dualize and twist a stack of N black D-branes to find a Melvin Universe supported by the flux of the NSNS b-field, which describes a non-comutative spacetime. It also shows that the spatial noncommutativity does not modify the scrambling time and will enhance the mutual information. We also study the corrected mutual information in the backreaction geometry due to the shock wave in our three model spacetimes.

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arXiv2016

Generalized Gravitational Entropy from Various Matter Fields

The generalized gravitational entropy proposed in recent by Lewkowycz and Maldacena [1] is extended to the systems of Boson fields, Fermion fields and Maxwell fields which have arbitrary frequency and mode numbers on the BTZ spacetime. We find the associated regular wave solution in each case and use it to calculate the exact gravitational entropy. The results show that there is a threshold frequency below which the Fermion fields could not contribute the generalized gravitational entropy. Also, the static and zero-mode solutions have no entropy, contrast to that in scalar fields. We also find that the entropy of the static scalar fields and non-static fermions is an increasing function of mode numbers and, after arriving the maximum entropy, it becomes a deceasing function approaching to a constant value. We calculate the gravitational entropy of Maxwell fields and use the duality between EM and scalar fields to explain its result. The gravitational entropy from DBI action is also studied.

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arXiv2016

Back-Reaction of Classical Fields on Black Hole Area Law

(This is the unpublished manuscript while parts are corrected and included in version III of arXiv:1602.00964 which is submitted to the journal.) We study the back-reaction of classical Maxwell field and massive scalar field on the BTZ black hole entropy. The exact values of the modification which correct the black hole area law are found. We discuss the similar properties between the scalar and Maxwell fields which are investigated in both of Coulomb gauge and Lorentz gauge. The dependences of mass and mode number on the black hole entropy are illustrated. We also study the back-reaction by D branes, which are described by DBI action, and explicitly check that the classical solution which gives the black hole entropy precisely corrects the black hole area law. Our results extend the calculations of the generalized gravitational entropy proposed in recent by Lewkowycz and Maldacena [1].

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arXiv2015

Landau Free Energy and Analytic Tricritical Point in Holographic Superfluid

We investigate the analytical method in studying the holographic superfluid model which is described by Maxwell field minimally coupling to a charged scalar field in a fixed AdS black hole background. We propose a method that enables us to find exact value of coefficient in the solution and thus obtain higher-order expansion of the associated Landau free energy of the holographic superfluid with flow. We determine the critical value of superfluid velocity at the tricritical point of holographic superfluid and compare it with the numerical value.

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arXiv2014

Generalized Gravitational Entropy of Interacting Scalar Field and Maxwell Field

The generalized gravitational entropy proposed by Lewkowycz and Maldacena in recent is extended to the interacting real scalar field and Maxwell field system. Using the BTZ geometry we first investigate the case of free real scalar field and then show a possible way to calculate the entropy of the interacting scalar field. Next, we investigate the Maxwell field system. We exactly solve the wave equation and calculate the analytic value of the generalized gravitational entropy. We also use the Einstein equation to find the effect of backreaction of the Maxwell field on the area of horizon. The associated modified area law is consistent with the generalized gravitational entropy.

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arXiv2013

Analytic Study of First-Order Phase Transition in Holographic Superconductor and Superfluid

We use the matching method to investigate the first-order phase transition in holographic superconductor and superfluid. We first use the simple holographic superconductor model to describe the matching method and mention how to see the first-order phase transition. Next, we study the holographic superconductor with Stückelberg term and see that the analytic results indicate the existence of first-order phase transition. Finally, we study the holographic superfluid and show that the first-order phase transition can be found for some values of parameters. We determine the critical value analytically and compare it with the previous numerical result.

hep-th↗

arXiv2013

Lorentz Covariant Lagrangians of Self-dual Gauge Fields

We extend the method of PST formulation to find a systematic way to covariantize several non-covariant Lagrangians of self-dual gauge fields. We derive in detail the necessary basic formulas which are used to prove the existence of extra local symmetry that allows us to gauge fix the auxiliary fields therein and non-covariant formulations are restored. We see that, the extra local symmetry in the PST and PSST formulations, which describe the covariant Lagrangians in the 6D decomposition of $6=1+5$ and $6=3+3$ respectively, can be expressed as a simple linear form in the field strength. However, although in this paper we have found the covariant Lagrangians in the other decomposition of $6=2+4$, the extra local symmetry of the gauge field cannot be expressed as a simple linear form in the field strength. We present a no-go theorem to prove this specific property. We also find other covariant Lagrangians with more complex decomposition of spacetime.

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