arXiv subjects

Chao Niu

Publications and source records attributed to Chao Niu.

At least 55 records · Page 3Linked to original sources

arXiv2017

Comparison of holographic and field theoretic complexities by time dependent thermofield double states

We compute the time-dependent complexity of the thermofield double states by four different proposals: two holographic proposals based on the "complexity-action" (CA) conjecture and "complexity-volume" (CV) conjecture, and two quantum field theoretic proposals based on the Fubini-Study metric (FS) and Finsler geometry (FG). We find that four different proposals yield both similarities and differences, which will be useful to deepen our understanding on the complexity and sharpen its definition. In particular, at early time the complexity linearly increase in the CV and FG proposals, linearly decreases in the FS proposal, and does not change in the CA proposal. In the late time limit, the CA, CV and FG proposals all show that the growth rate is $2E/(π\hbar)$ saturating the Lloyd's bound, while the FS proposal shows the growth rate is zero. It seems that the holographic CV conjecture and the field theoretic FG method are more correlated.

hep-th↗

arXiv2017

Surface Counterterms and Regularized Holographic Complexity

The holographic complexity is UV divergent. As a finite complexity, we propose a "regularized complexity" by employing a similar method to the holographic renormalization. We add codimension-two boundary counterterms which do not contain any boundary stress tensor information. It means that we subtract only non-dynamic background and all the dynamic information of holographic complexity is contained in the regularized part. After showing the general counterterms for both CA and CV conjectures in holographic spacetime dimension 5 and less, we give concrete examples: the BTZ black holes and the four and five dimensional Schwarzschild AdS black holes. We propose how to obtain the counterterms in higher spacetime dimensions and show explicit formulas only for some special cases with enough symmetries. We also compute the complexity of formation by using the regularized complexity.

hep-th↗

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.

hep-th↗

arXiv2017

Diffusion and Butterfly Velocity at Finite Density

We study diffusion and butterfly velocity ($v_B$) in two holographic models, linear axion and axion-dilaton model, with a momentum relaxation parameter ($β$) at finite density or chemical potential ($μ$). Axion-dilaton model is particularly interesting since it shows linear-$T$-resistivity, which may have something to do with the universal bound of diffusion. At finite density, there are two diffusion constants $D_\pm$ describing the coupled diffusion of charge and energy. By computing $D_\pm$ exactly, we find that in the incoherent regime ($β/T \gg 1,\ β/μ\gg 1$) $D_+$ is identified with the charge diffusion constant ($D_c$) and $D_-$ is identified with the energy diffusion constant ($D_e$). In the coherent regime, at very small density, $D_\pm$ are `maximally' mixed in the sense that $D_+(D_-)$ is identified with $D_e(D_c)$, which is opposite to the case in the incoherent regime. In the incoherent regime $D_e \sim C_- \hbar v_B^2 / k_B T$ where $C_- = 1/2$ or 1 so it is universal independently of $β$ and $μ$. However, $D_c \sim C_+ \hbar v_B^2 / k_B T$ where $C_+ = 1$ or $ β^2/16π^2 T^2$ so, in general, $C_+$ may not saturate to the lower bound in the incoherent regime, which suggests that the characteristic velocity for charge diffusion may not be the butterfly velocity. We find that the finite density does not affect the diffusion property at zero density in the incoherent regime.

hep-th↗

arXiv2016

Homes' law in Holographic Superconductor with Q-lattices

Homes' law, $ρ_s = C σ_{\mathrm{DC}} T_c$, is an empirical law satisfied by various superconductors with a material independent universal constant $C$, where $ρ_{s}$ is the superfluid density at zero temperature, $T_c$ is the critical temperature, and $σ_{\mathrm{DC}}$ is the electric DC conductivity in the normal state close to $T_c$. We study Homes' law in holographic superconductor with Q-lattices and find that Homes' law is realized for some parameter regime in insulating phase near the metal-insulator transition boundary, where momentum relaxation is strong. In computing the superfluid density, we employ two methods: one is related to the infinite DC conductivity and the other is related to the magnetic penetration depth. With finite momentum relaxation both yield the same results, while without momentum relaxation only the latter gives the superfluid density correctly because the former has a spurious contribution from the infinite DC conductivity due to translation invariance.

hep-th↗

arXiv2016

Generation and Detection of Surface Plasmon Polaritons by Transition Metal Dichalcogenides for Chip-level Electronic-Photonic Integrated Circuits

The monolithic integration of electronics and photonics has attracted enormous attention due to its potential applications. However, the realization of such hybrid circuits has remained a challenge because it requires optical communication at nanometer scales. A major challenge to this integration is the identification of a suitable material. After discussing the material aspect of the challenge, we identified atomically thin transition metal dichalcogenides (TMDs) as a perfect material platform to implement the circuit. The selection of TMDs is based on their very distinct property: monolayer TMDs are able to emit and absorb light at the same wavelength determined by direct exciton transitions. To prove the concept, we fabricated simple devices consisting of silver nanowires as plasmonic waveguides and monolayer TMDs as active optoelectronic media. Using photoexcitation, direct optical imaging and spectral analysis, we demonstrated generation and detection of surface plasmon polaritons by monolayer TMDs. Regarded as novel materials for electronics and photonics, transition metal dichalcogenides are expected to find new applications in next generation integrated circuits.

cond-mat.mes-hall↗

arXiv2016

Holographic Entanglement Entropy Close to Quantum Phase Transitions

We investigate the holographic entanglement entropy (HEE) of a strip geometry in four dimensional Q-lattice backgrounds, which exhibit metal-insulator transitions in the dual field theory. Remarkably, we find that the HEE always displays a peak in the vicinity of the quantum critical points. Our model provides the first direct evidence that the HEE can be used to characterize the quantum phase transition (QPT). We also conjecture that the maximization behavior of HEE at quantum critical points would be universal in general holographic models.

hep-th↗

arXiv2016

Universal corner contributions to entanglement negativity

It has been realised that corners in entangling surfaces can induce new universal contributions to the entanglement entropy and Rényi entropy. In this paper we study universal corner contributions to entanglement negativity in three- and four-dimensional CFTs using both field theory and holographic techniques. We focus on the quantity $χ$ defined by the ratio of the universal part of the entanglement negativity over that of the entanglement entropy, which may characterise the amount of distillable entanglement. We find that for most of the examples $χ$ takes bigger values for singular entangling regions, which may suggest increase in distillable entanglement. However, there also exist counterexamples where distillable entanglement decreases for singular surfaces. We also explore the behaviour of $χ$ as the coupling varies and observe that for singular entangling surfaces, the amount of distillable entanglement is mostly largest for free theories, while counterexample exists for free Dirac fermion in three dimensions. For holographic CFTs described by higher derivative gravity, $χ$ may increase or decrease, depending on the sign of the relevant parameters. Our results may reveal a more profound connection between geometry and distillable entanglement.

hep-th↗

arXiv2016

The pseudo-gap phase and the duality in holographic fermionic system with dipole coupling on Q-lattice

We classify the different phases by the "pole-zero mechanism" for a holographic fermionic system which contains a dipole coupling with strength $p$ on a Q-lattice background. A complete phase structure in $p$ space can be depicted in terms of Fermi liquid, non-Fermi liquid, Mott phase and pseudo-gap phase. In particular, we find that in general the region of the pseudo-gap phase in $p$ space is suppressed when the Q-lattice background is dual to a deep insulating phase, while for an anisotropic background, we have an anisotropic region for the pseudo-gap phase in $p$ space as well. In addition, we find that the duality between zeros and poles always exists regardless of whether or not the model is isotropic.

hep-th↗

arXiv2016

Note on Zero Temperature Holographic Superfluids

In this note, we have addressed various issues on zero temperature holographic superfluids. First, inspired by our numerical evidence for the equality between the superfluid density and particle density, we provide an elegant analytic proof for this equality by a boost trick. Second, using not only the frequency domain analysis but also the time domain analysis from numerical relativity, we identify the hydrodynamic normal modes and calculate out the sound speed, which is shown to increase with the chemical potential and saturate to the value predicted by the conformal field theory in the large chemical potential limit. Third, the generic non-thermalization is demonstrated by the fully non-linear time evolution from a non-equilibrium state for our zero temperature holographic superfluid. Furthermore, a conserved Noether charge is proposed in support of this behavior.

hep-th↗

arXiv2016

Modave Lectures on Applied AdS/CFT with Numerics

These lecture notes are intended to serve as an introduction to applied AdS/CFT with numerics for an audience of graduate students and others with little background in the subject. The presentation begins with a poor man's review of current status of quantum gravity, where AdS/CFT correspondence is believed to be the well formulated quantum gravity in the anti-de Sitter space. Then we present the basic ingredients in applied AdS/CFT and introduce the relevant numerics for solving differential equations into which the bulk dynamics collapses. To demonstrate how to apply AdS/CFT with numerics, we take the zero temperature holographic superfluid as a concrete example for case study. In passing, we also present some new results, which include the numerical evidence as well as an elegant analytic proof for the equality between the superfluid density and particle density, namely $ρ_s=ρ$, and the saturation to the predicted value $\frac{1}{\sqrt{2}}$ by conformal field theory for the sound speed in the large chemical potential limit.

gr-qc↗

arXiv2015

Holographic Thermal Relaxation in Superfluid Turbulence

Holographic duality provides a first-principles approach to investigate real time processes in quantum many-body systems, in particular at finite temperature and far-from-equilibrium. We use this approach to study the dynamical evolution of vortex number in a two-dimensional (2D) turbulent superfluid through numerically solving its gravity dual. We find that the temporal evolution of the vortex number can be well fit statistically by two-body decay due to the vortex pair annihilation featured relaxation process, thus confirm the previous suspicion based on the experimental data for turbulent superfluid in highly oblate Bose-Einstein condensates. Furthermore, the decay rate near the critical temperature is in good agreement with the recently developed effective theory of 2D superfluid turbulence.

hep-th↗

arXiv2015

Thermoelectric conductivities, shear viscosity, and stability in an anisotropic linear axion model

We study thermoelectric conductivities and shear viscosities in a holographically anisotropic model, which is dual to a spatially anisotropic $\mathcal{N}=4$ super-Yang-Mills theory at finite chemical potential. Momentum relaxation is realized through perturbing the linear axion field. Ac conductivity exhibits a coherent/incoherent metal transition. Deviations from the Wiedemann-Franz law are also observed in our model. The longitudinal shear viscosity for prolate anisotropy violates the bound conjectured by Kovtun-Son-Starinets. We also find that thermodynamic and dynamical instabilities are not always equivalent by examining the Gubser-Mitra conjecture.

hep-th↗

arXiv2015

Building a doped Mott system by holography

We construct a holographic model in the framework of Q-lattices whose dual exhibits metal-insulator transitions. By introducing an interacting term between the Q-lattice and the electromagnetic field in bulk geometry, we find such kind of transition can be Mott-like. The evidences are presented as follows. i) The transition from a metallic phase to an insulating phase occurs when the lattice constant becomes larger. ii) A hard gap in the insulating phase can be manifestly observed in the optical conductivity. Nevertheless, in the zero temperature limit this model exhibits novel metallic behavior, featured by a gap as well as a zero-frequency mode with tiny spectral weight. It implies that our model is dual to a doped Mott system in one dimension where umklapp scattering is frozen at zero temperature. The similarity between this model and some organic linear chain conductors is briefly discussed.

hep-th↗

arXiv2015

Holographic Superconductor on Q-lattice

We construct the simplest gravitational dual model of a superconductor on Q-lattices. We analyze the condition for the existence of a critical temperature at which the charged scalar field will condense. In contrast to the holographic superconductor on ionic lattices, the presence of Q-lattices will suppress the condensate of the scalar field and lower the critical temperature. In particular, when the Q-lattice background is dual to a deep insulating phase, the condensation would never occur for some small charges. Furthermore, we numerically compute the optical conductivity in the superconducting regime. It turns out that the presence of Q-lattice does not remove the pole in the imaginary part of the conductivity, ensuring the appearance of a delta function in the real part. We also evaluate the gap which in general depends on the charge of the scalar field as well as the Q-lattice parameters. Nevertheless, when the charge of the scalar field is relatively large and approaches the probe limit, the gap becomes universal with $ω_g \simeq 9T_c$ which is consistent with the result for conventional holographic superconductors.

hep-th↗

arXiv2014

Holographic fermionic system with dipole coupling on Q-lattice

We construct a holographic model for a fermionic system on Q-lattice and compute the spectral function in the presence of a dipole coupling. Both key features of doped Mott insulators, the dynamical generation of a gap and spectral weight transfer, are observed when adjusting the value of the coupling parameter $p$. Of particular interest is that when the background is in a deep insulating phase, the Mott gap opens much easier with a smaller coupling parameter in comparison with a metallic background. The effects of lattice parameters on the width of the gap $Δ/μ$ are studied and a turning point is observed near the critical regime of metal-insulator transitions of the background. Furthermore, the temperature dependence of the spectral function is studied. Finally, we also observe that the anisotropic Q-lattice generates anisotropic peaks with different magnitudes, indicating that insulating and metallic phases arise in different directions.

hep-th↗

arXiv2014

The Petrov-like boundary condition at finite cutoff surface in Gravity/Fluid duality

Previously it has been shown that imposing a Petrov-like boundary condition on a hypersurface may reduce the Einstein equation to the incompressible Navier-Stokes equation, but all these correspondences are established in the near horizon limit. In this note, we remark that this strategy can be extended to an arbitrary finite cutoff surface which is spatially flat, and the Navier-Stokes equation is obtained by employing a non-relativistic long-wavelength limit.

gr-qc↗

arXiv2014

Metal-insulator Transition by Holographic Charge Density Waves

We construct a gravity dual for charge density waves (CDW) in which the translational symmetry along one spatial direction is spontaneously broken. Our linear perturbation calculation on the gravity side produces the frequency dependence of the optical conductivity, which exhibits the two familiar features of charge density waves, namely the pinned collective mode and gapped single-particle excitation. These two features indicate that our gravity dual also provides a new mechanism to implement the metal to insulator phase transition by CDW, which is further supported by the fact that d.c. conductivity decreases with the decreased temperature below the critical temperature.

hep-th↗