scholarly journals Massive Corrections to Entanglement in Minimal E8 Toda Field Theory

2017 ◽  
Vol 2 (1) ◽  
Author(s):  
Olalla Castro-Alvaredo
Keyword(s):  
Field Theory ◽  
Bessel Functions ◽  
Entanglement Entropy ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Von Neumann Entropy ◽  
Numerical Work ◽  
Von Neumann ◽  
Twist Fields ◽  
Toda Field Theory

In this letter we study the exponentially decaying corrections to saturation of the second Rényi entropy of one interval of length \ellℓ in minimal E_8E8 Toda field theory. It has been known for some time that the entanglement entropy of a massive quantum field theory in 1+1 dimensions saturates to a constant value for m_1\ell\gg 1m1ℓ≫1 where m_1m1 is the mass of the lightest particle in the spectrum. Subsequently, results by Cardy, Castro-Alvaredo and Doyon have shown that there are exponentially decaying corrections to this behaviour which are characterized by Bessel functions with arguments proportional to m_1\ellm1ℓ. For the von Neumann entropy the leading correction to saturation takes the precise universal form -\frac{1}{8}K_0(2m_1\ell)−18K0(2m1ℓ) whereas for the Rényi entropies leading corrections which are proportional to K_0(m_1\ell)K0(m1ℓ) are expected. Recent numerical work by Pálmai for the second Rényi entropy of minimal E_8E8 Toda has identified next-to-leading order corrections which decay as e^{-2m_1\ell}e−2m1ℓ rather than the expected e^{-m_1\ell}e−m1ℓ. In this paper we investigate the origin of this result and show that it is incorrect. An exact form factor computation of correlators of branch point twist fields reveals that the leading corrections are proportional to K_0(m_1 \ell)K0(m1ℓ) as expected.

scholarly journals Entanglement entropy from TFD entropy operator

2021 ◽  
Vol 36 (13) ◽  
pp. 2150092
Author(s):  
M. Dias ◽  
Daniel L. Nedel ◽  
C. R. Senise
Keyword(s):  
Analytic Continuation ◽  
Moduli Space ◽  
Degrees Of Freedom ◽  
Entanglement Entropy ◽  
Expected Value ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Two Dimensional ◽  
Von Neumann

In this work, a canonical method to compute entanglement entropy is proposed. We show that for two-dimensional conformal theories defined in a torus, a choice of moduli space allows the typical entropy operator of the TFD to provide the entanglement entropy of the degrees of freedom defined in a segment and their complement. In this procedure, it is not necessary to make an analytic continuation from the Rényi entropy and the von Neumann entanglement entropy is calculated directly from the expected value of an entanglement entropy operator. We also propose a model for the evolution of the entanglement entropy and show that it grows linearly with time.

scholarly journals Rényi and von Neumann entropies of thermal state in Generalized Uncertainty Principle-corrected harmonic oscillator

2021 ◽  
Vol 36 (35) ◽  
Author(s):  
MuSeong Kim ◽  
Mi-Ra Hwang ◽  
Eylee Jung ◽  
DaeKil Park
Keyword(s):  
Harmonic Oscillator ◽  
Uncertainty Principle ◽  
Temperature Region ◽  
Thermal State ◽  
Generalized Uncertainty Principle ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Von Neumann Entropy ◽  
Large Temperature ◽  
Von Neumann

The Rényi and von Neumann entropies of thermal state in generalized uncertainty principle (GUP)-corrected single harmonic oscillator system are explicitly computed within the first order of GUP parameter [Formula: see text]. While the von Neumann entropy with [Formula: see text] exhibits a monotonically increasing behavior in external temperature, the nonzero GUP parameter makes a decreasing behavior at large temperature region. As a result, for the case of [Formula: see text], the von Neumann entropy is maximized at the finite temperature [Formula: see text]. The Rényi entropy [Formula: see text] with nonzero [Formula: see text] also exhibits similar behavior at large temperature region. In this region, the Rényi entropy exhibits a decreasing behavior with increasing temperature. The decreasing rate becomes larger when the order of the Rényi entropy is smaller.

scholarly journals Information Dynamic Correlation of Vibration in Nonlinear Systems

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 56
Author(s):  
Zhe Wu ◽  
Guang Yang ◽  
Qiang Zhang ◽  
Shengyue Tan ◽  
Shuyong Hou
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
System Dynamics ◽  
Mechanical Systems ◽  
Modal Identification ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Von Neumann Entropy ◽  
Identification System ◽  
Von Neumann

In previous studies, information dynamics methods such as Von Neumann entropy and Rényi entropy played an important role in many fields, covering both macroscopic and microscopic studies. They have a solid theoretical foundation, but there are few reports in the field of mechanical nonlinear systems. So, can we apply Von Neumann entropy and Rényi entropy to study and analyze the dynamic behavior of macroscopic nonlinear systems? In view of the current lack of suitable methods to characterize the dynamics behavior of mechanical systems from the perspective of nonlinear system correlation, we propose a new method to describe the nonlinear features and coupling relationship of mechanical systems. This manuscript verifies the above hypothesis by using a typical chaotic system and a real macroscopic physical nonlinear system through theory and practical methods. The nonlinear vibration correlation in multi-body mechanical systems is very complex. We propose a full-vector multi-scale Rényi entropy for exploring the chaos and correlation between the dynamic behaviors of mechanical nonlinear systems. The research results prove the effectiveness of the proposed method in modal identification, system dynamics evolution and fault diagnosis of nonlinear systems. It is of great significance to extend these studies to the field of mechanical nonlinear system dynamics.

scholarly journals Islands in linear dilaton black holes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Georgios K. Karananas ◽  
Alex Kehagias ◽  
John Taskas
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Entanglement Entropy ◽  
Von Neumann Entropy ◽  
Two Dimensional ◽  
Extremal Case ◽  
Von Neumann ◽  
Dimensional Black Hole ◽  
Linear Dilaton ◽  
Linear Dilaton Black Hole

Abstract We derive a novel four-dimensional black hole with planar horizon that asymptotes to the linear dilaton background. The usual growth of its entanglement entropy before Page’s time is established. After that, emergent islands modify to a large extent the entropy, which becomes finite and is saturated by its Bekenstein-Hawking value in accordance with the finiteness of the von Neumann entropy of eternal black holes. We demonstrate that viewed from the string frame, our solution is the two-dimensional Witten black hole with two additional free bosons. We generalize our findings by considering a general class of linear dilaton black hole solutions at a generic point along the σ-model renormalization group (RG) equations. For those, we observe that the entanglement entropy is “running” i.e. it is changing along the RG flow with respect to the two-dimensional worldsheet length scale. At any fixed moment before Page’s time the aforementioned entropy increases towards the infrared (IR) domain, whereas the presence of islands leads the running entropy to decrease towards the IR at later times. Finally, we present a four-dimensional charged black hole that asymptotes to the linear dilaton background as well. We compute the associated entanglement entropy for the extremal case and we find that an island is needed in order for it to follow the Page curve.

Generalized information and entanglement entropy, gravitation and holography

2015 ◽  
Vol 30 (16) ◽  
pp. 1530039 ◽  
Author(s):  
O. Obregón
Keyword(s):  
Entanglement Entropy ◽  
Ideal Gas ◽  
Einstein Equations ◽  
Von Neumann Entropy ◽  
Nonextensive Statistical Mechanics ◽  
Von Neumann ◽  
H Theorem ◽  
Gauge Gravity ◽  
Gravity Duality ◽  
Correction Terms

A nonextensive statistical mechanics entropy that depends only on the probability distribution is proposed in the framework of superstatistics. It is based on a Γ(χ2) distribution that depends on β and also on pl. The corresponding modified von Neumann entropy is constructed; it is shown that it can also be obtained from a generalized Replica trick. We further demonstrate a generalized H-theorem. Considering the entropy as a function of the temperature and volume, it is possible to generalize the equation of state of an ideal gas. Moreover, following the entropic force formulation a generalized Newton's law is obtained, and following the proposal that the Einstein equations can be deduced from the Clausius law, we discuss on the structure that a generalized Einstein's theory would have. Lastly, we address the question whether the generalized entanglement entropy can play a role in the gauge/gravity duality. We pay attention to 2d CFT and their gravity duals. The correction terms to the von Neumann entropy result more relevant than the usual UV ones and also than those due to the area dependent AdS3 entropy which result comparable to the UV ones. Then the correction terms due to the new entropy would modify the Ryu–Takayanagi identification between the CFT entanglement entropy and the AdS entropy in a different manner than the UV ones or than the corrections to the AdS3 area dependent entropy.

scholarly journals On the Exact Variance of Tsallis Entanglement Entropy in a Random Pure State

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 539 ◽  
Author(s):  
Lu Wei
Keyword(s):  
Pure State ◽  
Entanglement Entropy ◽  
Tsallis Entropy ◽  
Von Neumann Entropy ◽  
Quadratic Entropy ◽  
Von Neumann ◽  
Special Cases ◽  
Variance Formula ◽  
Finite Sums ◽  
Random Pure State

The Tsallis entropy is a useful one-parameter generalization to the standard von Neumann entropy in quantum information theory. In this work, we study the variance of the Tsallis entropy of bipartite quantum systems in a random pure state. The main result is an exact variance formula of the Tsallis entropy that involves finite sums of some terminating hypergeometric functions. In the special cases of quadratic entropy and small subsystem dimensions, the main result is further simplified to explicit variance expressions. As a byproduct, we find an independent proof of the recently proven variance formula of the von Neumann entropy based on the derived moment relation to the Tsallis entropy.

scholarly journals A field theory study of entanglement wedge cross section: odd entropy

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Ali Mollabashi ◽  
Kotaro Tamaoka
Keyword(s):  
Cross Section ◽  
Entanglement Entropy ◽  
Quantum Correlations ◽  
Von Neumann Entropy ◽  
Mixed States ◽  
Scale Invariant ◽  
Gaussian States ◽  
Von Neumann ◽  
Free Scalar ◽  
The Difference

Abstract We study odd entanglement entropy (odd entropy in short), a candidate of measure for mixed states holographically dual to the entanglement wedge cross section, in two-dimensional free scalar field theories. Our study is restricted to Gaussian states of scale-invariant theories as well as their finite temperature generalizations, for which we show that odd entropy is a well-defined measure for mixed states. Motivated from holographic results, the difference between odd and von Neumann entropy is also studied. In particular, we show that large amounts of quantum correlations ensure the odd entropy to be larger than von Neumann entropy, which is qualitatively consistent with the holographic CFT. In general cases, we also find that this difference is not even a monotonic function with respect to size of (and distance between) subsystems.

Aspects of Entropy Squeezing and Entanglement for Moving Two-Level Atom in Presence of Finite Trio Coherent State

2016 ◽  
Vol 13 (10) ◽  
pp. 7455-7459
Author(s):  
S. I Ali ◽  
A. M Mosallem ◽  
T Emam
Keyword(s):  
Entanglement Entropy ◽  
Photon Number ◽  
Atomic Motion ◽  
Von Neumann Entropy ◽  
Wehrl Entropy ◽  
Entropy Squeezing ◽  
Von Neumann ◽  
Special Values ◽  
Level Atom ◽  
Motion Parameters

In this paper, we investigate the entanglement of the interaction of three modes of radiation field with moving and unmoving two-level atom. The time evolution of the von Neumann entropy, entropy squeezing and marginal atomic Wehrl entropy is investigated. The marginal atomic Wehrl entropy as squeezing indicator of the entanglement of the system is suggested. The results beacon the important roles played by both the atomic motion parameters in the evolution of entanglement, entropy squeezing and marginal atomic Wehrl entropy. Using special values of the photon number of transition and atomic motion parameter, the entanglement phenomena of sudden death and long living entanglenment can be appeared. The results show that there is atomic motion monotonic harmonization atomic Wehrl entropy (WE). It is illustrated that the amount of the above-mentioned phenomena can be tuned by controlling the evolved parameters appropriately.

scholarly journals ENTANGLEMENT ENTROPY: HELICITY VERSUS SPIN

2008 ◽  
Vol 06 (01) ◽  
pp. 181-186 ◽  
Author(s):  
SONG HE ◽  
SHUXIN SHAO ◽  
HONGBAO ZHANG
Keyword(s):  
Density Matrix ◽  
Entanglement Entropy ◽  
Specific Form ◽  
Von Neumann Entropy ◽  
Particle State ◽  
Inertial Reference Frame ◽  
Helicity State ◽  
Von Neumann ◽  
Left Handed ◽  
Massive Spin

For a massive spin 1/2 field, we present the reduced spin and helicity density matrix, respectively, for the same pure one particle state. Their relation has also been developed. Furthermore, we calculate and compare the corresponding entanglement entropy for spin and helicity within the same inertial reference frame. Due to the distinct dependence on momentum degree of freedom between spin and helicity states, the resultant helicity entropy is different from that of spin in general. In particular, we find that both helicity entanglement for a spin eigenstate and spin entanglement for a right handed or left handed helicity state do not vanish, and their Von Neumann entropy has no dependence on the specific form of momentum distribution, as long as it is isotropic.

Sign in / Sign up

Export Citation Format

Share Document