scholarly journals Thermality and excited state Rényi entropy in two-dimensional CFT

2016 ◽  
Vol 2016 (11) ◽  
Author(s):  
Feng-Li Lin ◽  
Huajia Wang ◽  
Jia-ju Zhang
Keyword(s):  
Excited State ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Two Dimensional

scholarly journals Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part II. Multi-particle states

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Jiaju Zhang ◽  
M. A. Rajabpour
Keyword(s):  
Field Theory ◽  
Excited State ◽  
Excited States ◽  
Short Interval ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Two Dimensional ◽  
Bosonic Field ◽  
Conformal Field ◽  
Harmonic Chain

Abstract We study the excited state Rényi entropy and subsystem Schatten distance in the two-dimensional free massless non-compact bosonic field theory, which is a conformal field theory. The discretization of the free non-compact bosonic theory gives the harmonic chain with local couplings. We consider the field theory excited states that correspond to the harmonic chain states with excitations of more than one quasiparticle, which we call multi-particle states. This extends the previous work by the same authors to more general excited states. In the field theory we obtain the exact Rényi entropy and subsystem Schatten distance for several low-lying states. We obtain short interval expansion of the Rényi entropy and subsystem Schatten distance for general excited states, which display different universal scaling behaviors in the gapless and extremely gapped limits of the non-compact bosonic theory. In the locally coupled harmonic chain we calculate numerically the excited state Rényi entropy and subsystem Schatten distance using the wave function method. We find excellent matches of the analytical results in the field theory and numerical results in the gapless limit of the harmonic chain. We also make some preliminary investigations of the Rényi entropy and the subsystem Schatten distance in the extremely gapped limit of the harmonic chain.

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 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 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 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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