scholarly journals Particle number fluctuations, Rényi entropy, and symmetry-resolved entanglement entropy in a two-dimensional Fermi gas from multidimensional bosonization

2020 ◽  
Vol 101 (23) ◽  
Author(s):  
Mao Tian Tan ◽  
Shinsei Ryu
Keyword(s):  
Particle Number ◽  
Entanglement Entropy ◽  
Fermi Gas ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Two Dimensional

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 Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part I. Single-particle states

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jiaju Zhang ◽  
M.A. Rajabpour
Keyword(s):  
Excited States ◽  
Single Particle ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Large Momentum ◽  
Particle State ◽  
Two Dimensional ◽  
Universal Form ◽  
Conformal Field ◽  
Harmonic Chain

Abstract We investigate the Rényi entropy of the excited states produced by the current and its derivatives in the two-dimensional free massless non-compact bosonic theory, which is a two-dimensional conformal field theory. We also study the subsystem Schatten distance between these states. The two-dimensional free massless non-compact bosonic theory is the continuum limit of the finite periodic gapless harmonic chains with the local interactions. We identify the excited states produced by current and its derivatives in the massless bosonic theory as the single-particle excited states in the gapless harmonic chain. We calculate analytically the second Rényi entropy and the second Schatten distance in the massless bosonic theory. We then use the wave functions of the excited states and calculate the second Rényi entropy and the second Schatten distance in the gapless limit of the harmonic chain, which match perfectly with the analytical results in the massless bosonic theory. We verify that in the large momentum limit the single-particle state Rényi entropy takes a universal form. We also show that in the limit of large momenta and large momentum difference the subsystem Schatten distance takes a universal form but it is replaced by a new corrected form when the momentum difference is small. Finally we also comment on the mutual Rényi entropy of two disjoint intervals in the excited states of the two-dimensional free non-compact bosonic theory.

scholarly journals Infrared Electric Image Thresholding Using Two-Dimensional Fuzzy Renyi Entropy

2011 ◽  
Vol 12 ◽  
pp. 411-419 ◽  
Author(s):  
Songhai Fan ◽  
Shuhong Yang ◽  
Pu He ◽  
Hongyu Nie
Keyword(s):  
Renyi Entropy ◽  
Rényi Entropy ◽  
Two Dimensional ◽  
Image Thresholding ◽  
Electric Image

scholarly journals Semiclassical limit of topological Rényi entropy in 3d Chern-Simons theory

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Siddharth Dwivedi ◽  
Vivek Kumar Singh ◽  
Abhishek Roy
Keyword(s):  
Semiclassical Limit ◽  
Entanglement Entropy ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Simons Theory ◽  
Yang Mills ◽  
Rényi Entropies ◽  
Chern Simons ◽  
Chern Simons Theory ◽  
Torus Links

Abstract We study the multi-boundary entanglement structure of the state associated with the torus link complement S3\Tp,q in the set-up of three-dimensional SU(2)k Chern-Simons theory. The focal point of this work is the asymptotic behavior of the Rényi entropies, including the entanglement entropy, in the semiclassical limit of k → ∞. We present a detailed analysis of several torus links and observe that the entropies converge to a finite value in the semiclassical limit. We further propose that the large k limiting value of the Rényi entropy of torus links of type Tp,pn is the sum of two parts: (i) the universal part which is independent of n, and (ii) the non-universal or the linking part which explicitly depends on the linking number n. Using the analytic techniques, we show that the universal part comprises of Riemann zeta functions and can be written in terms of the partition functions of two-dimensional topological Yang-Mills theory. More precisely, it is equal to the Rényi entropy of certain states prepared in topological 2d Yang-Mills theory with SU(2) gauge group. Further, the universal parts appearing in the large k limits of the entanglement entropy and the minimum Rényi entropy for torus links Tp,pn can be interpreted in terms of the volume of the moduli space of flat connections on certain Riemann surfaces. We also analyze the Rényi entropies of Tp,pn link in the double scaling limit of k → ∞ and n → ∞ and propose that the entropies converge in the double limit as well.

scholarly journals Induced entanglement entropy of harmonic oscillators in non-commutative phase space

2019 ◽  
Vol 34 (33) ◽  
pp. 1950269
Author(s):  
Bingsheng Lin ◽  
Jian Xu ◽  
Taihua Heng
Keyword(s):  
Phase Space ◽  
Ground State ◽  
Entanglement Entropy ◽  
Harmonic Oscillators ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Wigner Functions ◽  
Definition Of

We study the entanglement entropy of harmonic oscillators in non-commutative phase space (NCPS). We propose a new definition of quantum Rényi entropy based on Wigner functions in NCPS. Using the Rényi entropy, we calculate the entanglement entropy of the ground state of the 2D isotropic harmonic oscillators. We find that for some values of the non-commutative parameters, the harmonic oscillators can be entangled in NCPS. This is a new entanglement-like effect caused by the non-commutativity of the phase space.

scholarly journals Correlation functions and quantum measures of descendant states

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm ◽  
Matteo Broccoli
Keyword(s):  
Differential Operator ◽  
Correlation Functions ◽  
Recursive Formula ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Two Dimensional ◽  
Computer Implementation ◽  
Point Function ◽  
Rényi Divergence ◽  
Holographic Description

Abstract We discuss a computer implementation of a recursive formula to calculate correlation functions of descendant states in two-dimensional CFT. This allows us to obtain any N-point function of vacuum descendants, or to express the correlator as a differential operator acting on the respective primary correlator in case of non-vacuum descendants. With this tool at hand, we then study some entanglement and distinguishability measures between descendant states, namely the Rényi entropy, trace square distance and sandwiched Rényi divergence. Our results provide a test of the conjectured Rényi QNEC and new tools to analyse the holographic description of descendant states at large c.

scholarly journals Rényi entropy of a line in two-dimensional Ising models

2010 ◽  
Vol 82 (12) ◽  
Author(s):  
J.-M. Stéphan ◽  
G. Misguich ◽  
V. Pasquier
Keyword(s):  
Ising Models ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Two Dimensional
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