arXiv subjects

Fu-Wen Shu

Publications and source records attributed to Fu-Wen Shu.

At least 55 records · Page 3Linked to original sources

arXiv2020

Quantum bit threads of MERA tensor network in large $c$ limit

The Ryu-Takayanagi (RT) formula is a crucial concept in current theory of gauge-gravity duality and emergent phenomena of geometry. Recent reinterpretation of this formula in terms of a set of "bit threads" is an interesting effort in understanding holography. In this paper, we investigate a quantum generalization of the "bit threads" based on tensor network, with particular interests in the multi-scale entanglement renormalization ansatz (MERA). We demonstrate that, in the large $c$ limit, isometries of the MERA can be regarded as "sources" (or "sinks") of the information flow, which extensively modifies the original picture of the bit threads by introducing a new variable $ρ$: density of the isometries. In this modified picture of information flow, the isometries can be viewed as generators of the flow. The strong subadditivity and related properties of the entanglement entropy are also obtained in this new picture. The large $c$ limit implies the classical gravity can be emerged from the information flow.

hep-th↗

arXiv2020

Vacua in novel 4D Einstein-Gauss-Bonnet Gravity: pathology and instability?

We show an inconsistence of the novel 4D Einstein-Gauss-Bonnet gravity by considering a quantum tunneling process of vacua. Using standard semi-classical techniques, we analytically study the vacuum decay rate for all allowed cases in the parameter space. It turns out, without exception, that the theory either encounters a disastrous divergence of vacuum decay rate, or exhibits a confusing complex value of vacuum decay rate, or involves an infinitely instability (a large vacuum mixing). These suggest a strong possibility that the theory, at least the vacuum of the theory, is either unphysical or unstable, or has no well-defined limit as $D\rightarrow 4$.

gr-qc↗

arXiv2019

Towards a Fisher-information description of complexity in de Sitter universe

Recent developments on holography and quantum information physics suggest that quantum information theory come to play a fundamental role in understanding quantum gravity. Cosmology, on the other hand, plays a significant role in testing quantum gravity effects. How to apply this idea to a realistic universe is still missing. Here we show some concepts in quantum information theory have their cosmological descriptions. Particularly, we show complexity of a tensor network can be regarded as a Fisher information measure(FIM) of a dS universe, followed by several observations: (i) the holographic entanglement entropy has a tensor-network description and admits a information-theoretical interpretation, (ii) on-shell action of dS spacetime has a same description of FIM, (iii) complexity/action(CA) duality holds for dS spacetime. Our result is also valid for $f(R)$ gravity, whose FIM exhibits the same features of a recent proposed $L^n$ norm complexity.

hep-th↗

arXiv2019

Bit threads and holographic entanglement of purification

The entanglement of purification (EoP), which measures the classical correlations and entanglement of a given mixed state, has been conjectured to be dual to the area of the minimal cross section of the entanglement wedge in holography. Using the surface-state correspondence, we propose a `bit thread' formulation of the EoP. With this formulation, proofs of some known properties of the EoP are performed. Moreover, we show that the quantum advantage of dense code (QAoDC), which reflects the increase in the rate of classical information transmission through quantum channel due to entanglement, also admits a flow interpretation. In this picture, we can prove the monogamy relation of QAoDC with the EoP for tripartite states. We also derive a new lower bound for $S(AB)$ in terms of QAoDC, which is tighter than the one given by the Araki-Lieb inequality.

hep-th↗

arXiv2018

Characterizing quantum phase transition by teleportation

In this paper we provide a novel way to explore the relation between quantum teleportation and quantum phase transition. We construct a quantum channel with a mixed state which is made from one dimensional quantum Ising chain with infinite length, and then consider the teleportation with the use of entangled Werner states as input qubits. The fidelity as a figure of merit to measure how well the quantum state is transferred is studied numerically. Remarkably we find the first-order derivative of the fidelity with respect to the parameter in quantum Ising chain exhibits a logarithmic divergence at the quantum critical point. The implications of this phenomenon and possible applications are also briefly discussed.

quant-ph↗

arXiv2018

Quantum information metric of conical defect

A concept of measuring the quantum distance between two different quantum states which is called quantum information metric is presented. The holographic principle (AdS/CFT) suggests that the quantum information metric $G_{λλ}$ between perturbed state and unperturbed state in field theory has a dual description in the classical gravity. In this work we calculate the quantum information metric of a theory which is dual to a conical defect geometry and we show that it is $n$ times the one of its covering space. We also give a holographic check for our result in the gravity side. Meanwhile, it was argued that $G_{λλ}$ is dual to a codimension-one surface in spacetime and satisfies $G_{λλ}=n_{d}\cdot\mbox{Vol}(Σ_{max})/L^{d}$. We show that the coefficient $n_d$ for conical defect should be rescaled by $n^2$ from the one for AdS. A limit case of conical defect --- the massless BTZ black hole--- is also considered. We show that the quantum information metric of the massless BTZ black hole disagrees with the one obtained by taking the vanishing temperature limit in BTZ black hole. This provides a new arena in differiating the different phases between BTZ spacetime and its massless cousin.

hep-th↗

arXiv2017

Holevo Bound of Entropic Uncertainty in Schwarzschild Spacetime

For a pair of incompatible quantum measurements, the total uncertainty can be bounded by a state-independent constant. However, such a bound can be violated if the quantum system is entangled with another quantum system (called memory); the quantum correlation between the systems can reduce the measurement uncertainty. On the other hand, in a curved spacetime, the presence of the Hawking radiation can increase the uncertainty in quantum measurement. The interplay of quantum correlation in the curved spacetime has become an interesting arena for studying quantum uncertainty relations. Here we demonstrate that the bounds of the entropic uncertainty relations, in the presence of memory, can be formulated in terms of the Holevo quantity, which limits how much information can be encoded in a quantum system. Specifically, we considered two examples with Dirac fields, near the event horizon of a Schwarzschild black hole, the Holevo bound provides a better bound than the previous bound based on the mutual information. Furthermore, if the memory moves away from the black hole, the difference between the total uncertainty and the Holevo bound remains a constant, not depending on any property of the black hole.

quant-ph↗

arXiv2017

Holography as deep learning

Quantum many-body problem with exponentially large degrees of freedom can be reduced to a tractable computational form by neural network method \cite{CT}. The power of deep neural network (DNN) based on deep learning is clarified by mapping it to renormalization group (RG), which may shed lights on holographic principle by identifying a sequence of RG transformations to the AdS geometry. In this essay, we show that any network which reflects RG process has intrinsic hyperbolic geometry, and discuss the structure of entanglement encoded in the graph of DNN. We find the entanglement structure of deep neural network is of Ryu-Takayanagi form. Based on these facts, we argue that the emergence of holographic gravitational theory is related to deep learning process of the quantum field theory.

gr-qc↗

arXiv2017

Charged Lifshitz black hole and probed Lorentz-violation fermions from holography

We analytically obtain a new charged Lifshtitz solution by adding a non-relativistic Maxwell field in Horava-Lifshitz gravity. The black hole exhibits an anisotropic scaling between space and time (Lifshitz scaling) in the UV limit, while in the IR limit, the Lorentz invariance is recovered. We introduce the probed Lorentz-violation fermions into the background and holographically investigate the spectral properties of the dual fermionic operator. The Lorentz-violation of fermions will enhance the peak and corresponds larger fermi momentum, which compensates the non-relativistic bulk effect of the dynamical exponent. For a fixed $z$, when the Lorentz-violation of fermions increases to a critical value, the behavior of the low energy excitation goes from a non-Fermi liquid type to a fermi liquid type, which implies a kind of phase transition.

hep-th↗

arXiv2017

Holographic complexity: A tool to probe the property of reduced fidelity susceptibility

Quantum information theory along with holography play central roles in our understanding of quantum gravity. Exploring their connections will lead to profound impacts on our understanding of the modern physics and is thus a key challenge for present theory and experiments. In this paper, we investigate a recent conjectured connection between reduced fidelity susceptibility and holographic complexity (the RFS/HC duality for short). We give a quantitative proof of the duality by performing both holographic and field theoretical computations. In addition, holographic complexity in $AdS_{2+1}$ are explored and several important properties are obtained. These properties allow us, via the RFS/HC duality, to obtain a set of remarkable identities of the reduced fidelity susceptibility, which may have significant implications for our understanding of the reduced fidelity susceptibility. Moreover, utilizing these properties and the recent proposed diagnostic tool based on the fidelity susceptibility, experimental verification of the RFS/HC duality becomes possible.

hep-th↗

arXiv2016

Emergent geometry, thermal CFT and surface/state correspondence

We study a conjectured correspondence between any codimension two convex surface and a quantum state (SS-duality for short). By generalizing thermofield double formalism to continuum version of the multi-scale entanglement renormalization ansatz (cMERA) and using the SS-duality, we show that thermal geometries naturally emerge as a result of hidden quantum entanglement between boundary CFTs. We therefore propose a general framework to emerge the thermal geometry from CFT at finite temperature. As an example, the case of $2d$ CFT is considered. We calculate its information metric and show that it is either BTZ black hole or thermal AdS as expected.

hep-th↗

arXiv2016

Lifshitz holographic superconductor in Horava-Lifshitz gravity

We study the holographic phase transition of superconductor dual to a Lifshitz black brane probed by an anisotropic scalar field in the probe limit in Hourava-Lifshitz gravity. With the use of numerical and analytical method, we investigate how the critical temperature of the condensation is affected by the Lifshitz exponent $z$, $α-$correction term in the action as well as the dimensions of the gravity. We also numerically explore the condensation of the dual operator and optical conductivity of the holographic system. Various interesting properties of the holographic condensation affected by the parameters of model are discussed.

hep-th↗

arXiv2016

Thermal geometry from CFT at finite temperature

We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of $2d$ CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking-Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.

hep-th↗

arXiv2016

Crystalline geometries from fermionic vortex lattice with hyperscaling violation

We analytically consider the spontaneous formation of a fermionic crystalline geometry in a gravity background with Lifshitz scaling and/or hyperscaling violation. Fermionic vortex lattice solution sourced by the lowest Laundau level has been obtained. Thermodynamic analysis shows that the fermionic vortex lattice favors a triangular configuration, regardless of the values of the Lifshitz scaling $z$ and the hyperscaling violation exponent $θ$. Our results also show that the larger $z$ or lower $θ$ leads to more stable lattices thermodynamically.

hep-th↗

arXiv2015

High-dimensional Lifshitz-type spacetimes, universal horizons and black holes in Hořava-Lifshitz gravity

In this paper, we present all $[(d+1)+1]$-dimensional static diagonal vacuum solutions of the non-projectable Hořava-Lifshitz gravity in the IR limit, and show that they give rise to very rich Lifshitz-type structures, depending on the choice of the free parameters of the solutions. These include the Lifshitz spacetimes with or without hyperscaling violation, Lifshitz solitons, and black holes. Remarkably, even the theory breaks explicitly the Lorentz symmetry and allows generically instantaneous propagations, universal horizons still exist, which serve as one-way membranes for signals with any large velocities. In particular, particles even with infinitely large velocities would just move around on these boundaries and cannot escape to infinity. Another remarkable feature appearing in the Lifshitz-type spacetimes is that the dynamical exponent $z$ can take its values only in the ranges $1 \le z < 2$ for $d \ge 3$ and $1 \le z <\infty$ for $d = 2$, due to the stability and ghost-free conditions of the theory.

hep-th↗

arXiv2015

A holographic model of d-wave superconductor vortices with Lifshitz scaling

We study analytically the $d$-wave holographic superconductors with Lifshitz scaling in the presence of external magnetic field. The vortex lattice solutions of the model have also been obtained with different Lifshitz scaling. Our results imply that holographic $d$-wave superconductor is indeed a type II one even for different Lifshitz scaling. This is the same as the conventional $d$-wave superconductors in the Ginzburg-Landau theory. Our results also indicate that the dynamical exponent $z$ has no effect to the shape of the vortex lattice even after higher order corrections (away from the phase transition point $B_c$) are included. However, it has effects on the upper critical magnetic field $B_{c_2}$ through the fact that a larger $z$ results in a smaller $B_{c_2}$ and therefore influences the size (characterized by $r_0\equiv 1/\sqrt{B_{c_2}}$) of the vortex lattices. Furthermore, close comparisons between our results and those of the Ginzburg-Landau theory reveal the fact that the upper critical magnetic field $B_{c_2}$ is inversely proportional to the square of the superconducting coherence length $ξ$, regardless of the anisotropy between space and time.

hep-th↗

arXiv2014

Causality Constraint on Noncritical Einstein-Weyl Gravity

We explore, in the context of AdS/CFT correspondence, the causality constraints on the Noncritical Einstein-Weyl (NEW) gravity model in five dimensions. The scalar and shear channels are considered as small metric perturbations around an AdS black brane background. Our results show that causality analysis on the propagation of these two channels imposes a new bound on the coupling of the Weyl-squared terms in the NEW gravity. This new bound imposes more stringent restrictions than those of the tachyon-free condition, improving predictive power of the theory.

hep-th↗

arXiv2014

Lifshitz spacetimes, solitons, and generalized BTZ black holes in quantum gravity at a Lifshitz point

In this paper, we study static vacuum solutions of quantum gravity at a fixed Lifshitz point in (2+1) dimensions, and present all the diagonal solutions in closed forms in the infrared limit. The exact solutions represent spacetimes with very rich structures: they can represent generalized BTZ black holes, Lifshitz space-times or Lifshitz solitons, in which the spacetimes are free of any kind of space-time singularities, depending on the choices of the free parameters of the solutions. We also find several classes of exact static non-diagonal solutions, which represent similar space-time structures as those given in the diagonal case. The relevance of these solutions to the non-relativistic Lifshitz-type gauge/gravity duality is discussed.

hep-th↗