scholarly journals Essential singularity in the Renyi entanglement entropy of the one-dimensionalXYZspin-12chain

2011 ◽  
Vol 83 (1) ◽  
Author(s):  
Elisa Ercolessi ◽  
Stefano Evangelisti ◽  
Fabio Franchini ◽  
Francesco Ravanini
Keyword(s):  
Entanglement Entropy ◽  
Essential Singularity ◽  
The One

scholarly journals Monodromy defects in free field theories

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Lorenzo Bianchi ◽  
Adam Chalabi ◽  
Vladimír Procházka ◽  
Brandon Robinson ◽  
Jacopo Sisti
Keyword(s):  
Entanglement Entropy ◽  
Free Field ◽  
Operator Product ◽  
Dirac Fermions ◽  
Maxwell Theory ◽  
Conformal Field ◽  
Defect Operator ◽  
Crucial Information ◽  
The One ◽  
Group Flow

Abstract We study co-dimension two monodromy defects in theories of conformally coupled scalars and free Dirac fermions in arbitrary d dimensions. We characterise this family of conformal defects by computing the one-point functions of the stress-tensor and conserved current for Abelian flavour symmetries as well as two-point functions of the displacement operator. In the case of d = 4, the normalisation of these correlation functions are related to defect Weyl anomaly coefficients, and thus provide crucial information about the defect conformal field theory. We provide explicit checks on the values of the defect central charges by calculating the universal part of the defect contribution to entanglement entropy, and further, we use our results to extract the universal part of the vacuum Rényi entropy. Moreover, we leverage the non-supersymmetric free field results to compute a novel defect Weyl anomaly coefficient in a d = 4 theory of free $$ \mathcal{N} $$ N = 2 hypermultiplets. Including singular modes in the defect operator product expansion of fundamental fields, we identify notable relevant deformations in the singular defect theories and show that they trigger a renormalisation group flow towards an IR fixed point with the most regular defect OPE. We also study Gukov-Witten defects in free d = 4 Maxwell theory and show that their central charges vanish.

scholarly journals Generic Entanglement Entropy for Quantum States with Symmetry

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 684
Author(s):  
Yoshifumi Nakata ◽  
Mio Murao
Keyword(s):  
Phase Transition ◽  
Information Science ◽  
Entanglement Entropy ◽  
Quantum States ◽  
Permutation Symmetry ◽  
Phase Transition Behavior ◽  
Bipartite Entanglement ◽  
Translation Symmetry ◽  
The One ◽  
Random States

When a quantum pure state is drawn uniformly at random from a Hilbert space, the state is typically highly entangled. This property of a random state is known as generic entanglement of quantum states and has been long investigated from many perspectives, ranging from the black hole science to quantum information science. In this paper, we address the question of how symmetry of quantum states changes the properties of generic entanglement. More specifically, we study bipartite entanglement entropy of a quantum state that is drawn uniformly at random from an invariant subspace of a given symmetry. We first extend the well-known concentration formula to the one applicable to any subspace and then show that 1. quantum states in the subspaces associated with an axial symmetry are still highly entangled, though it is less than that of the quantum states without symmetry, 2. quantum states associated with the permutation symmetry are significantly less entangled, and 3. quantum states with translation symmetry are as entangled as the generic one. We also numerically investigate the phase-transition behavior of the distribution of generic entanglement, which indicates that the phase transition seems to still exist even when random states have symmetry.

scholarly journals COSMIC HOLOGRAPHIC BOUNDS WITH UV AND IR CUTOFFS

2005 ◽  
Vol 20 (27) ◽  
pp. 2035-2046 ◽  
Author(s):  
YUN SOO MYUNG
Keyword(s):  
Dark Energy ◽  
Entanglement Entropy ◽  
Planck Scale ◽  
Inflationary Universe ◽  
Future Event ◽  
The Past ◽  
Slow Roll ◽  
Energy Bound ◽  
The One ◽  
Future Event Horizon

We introduce the cosmic holographic bounds with two uv and ir cutoff scales, to deal with both the inflationary universe in the past and dark energy in the future. To describe quantum fluctuations of inflation on sub-horizon scales, we use the Bekenstein–Hawking energy bound. The Hubble bounds are introduced for classical fluctuations of inflation on super-horizon scales. It turns out that the Hubble entropy bound is satisfied with the entanglement entropy and the Hubble temperature bound leads to a condition for the slow-roll inflation. In order to describe the dark energy, we introduce the holographic energy density which is the one saturating the Bekenstein–Hawking energy bound for a weakly gravitating system. Here the uv (ir) cutoff is given by the Planck scale (future event horizon), respectively. As a result, we find the close connection between inflation and dark energy.

scholarly journals Fidelity and entanglement entropy in the one-dimensional transverse-field quantum compass model

2013 ◽  
Vol 88 (1) ◽  
pp. 015003 ◽  
Author(s):  
Mostafa Motamedifar ◽  
Saeed Mahdavifar ◽  
Saber Farjami Shayesteh ◽  
Somayyeh Nemati
Keyword(s):  
Entanglement Entropy ◽  
Transverse Field ◽  
One Dimensional ◽  
The One

scholarly journals Holographic renormalization group flow effect on quantum correlations

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Chanyong Park ◽  
Jung Hun Lee
Keyword(s):  
Entanglement Entropy ◽  
Finite Size ◽  
Quantum Correlations ◽  
Scaling Effects ◽  
Point Function ◽  
Holographic Renormalization ◽  
Geodesic Length ◽  
Local Operators ◽  
The One ◽  
Group Flow

Abstract We holographically study the finite-size scaling effects on macroscopic and microscopic quantum correlations deformed by excitation and condensation. The excitation (condensation) increases (decreases) the entanglement entropy of the system. We also investigate the two-point correlation function of local operators by calculating the geodesic length connecting two local operators. As opposed to the entanglement entropy case, the excitation (condensation) decreases (increases) the two-point function. This is because the screening effect becomes strong in the background with the large entanglement entropy. We further show that the holographic renormalization leads to the qualitatively same two-point function as the one obtained from the geodesic length.

scholarly journals ENTANGLEMENT ENTROPY AND QUANTUM FIELD THEORY: A NON-TECHNICAL INTRODUCTION

2006 ◽  
Vol 04 (03) ◽  
pp. 429-438 ◽  
Author(s):  
PASQUALE CALABRESE ◽  
JOHN CARDY
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Entanglement Entropy ◽  
Quantum Critical Point ◽  
Theory Approach ◽  
Quantum Field ◽  
Linear Dispersion ◽  
Conformal Field ◽  
Linear Dispersion Relation ◽  
The One

We give a pedagogical and non-technical introduction to the quantum field theory approach to entanglement entropy. Particular attention is devoted to the one space dimensional case, with a linear dispersion relation, that, at a quantum critical point, can be effectively described by a two-dimensional conformal field theory.

scholarly journals A falling magnetic monopole as a holographic local quench

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Nicolò Zenoni ◽  
Roberto Auzzi ◽  
Stefania Caggioli ◽  
Maria Martinelli ◽  
Giuseppe Nardelli
Keyword(s):  
Black Hole ◽  
Boundary Conditions ◽  
Functional Form ◽  
Magnetic Monopole ◽  
Energy Momentum Tensor ◽  
Entanglement Entropy ◽  
Momentum Tensor ◽  
Negative Contribution ◽  
Monopole Solution ◽  
The One

Abstract An analytic static monopole solution is found in global AdS4, in the limit of small backreaction. This solution is mapped in Poincaré patch to a falling monopole configuration, which is dual to a local quench triggered by the injection of a condensate. Choosing boundary conditions which are dual to a time-independent Hamiltonian, we find the same functional form of the energy-momentum tensor as the one of a quench dual to a falling black hole. On the contrary, the details of the spread of entanglement entropy are very different from the falling black hole case, where the quench induces always a higher entropy compared to the vacuum, i.e. ∆S > 0. In the propagation of entanglement entropy for the monopole quench, there is instead a competition between a negative contribution to ∆S due to the scalar condensate and a positive one carried by the freely propagating quasiparticles generated by the energy injection.

scholarly journals Entanglement entropy and spectra of the one-dimensional Kugel-Khomskii model

2012 ◽  
Vol 86 (22) ◽  
Author(s):  
Rex Lundgren ◽  
Victor Chua ◽  
Gregory A. Fiete
Keyword(s):  
Entanglement Entropy ◽  
One Dimensional ◽  
The One
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