scholarly journals Highly Entangled Spin Chains and 2D Quantum Gravity

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 916
Author(s):  
Fumihiko Sugino
Keyword(s):  
Quantum Gravity ◽  
Spin Systems ◽  
Spin Chains ◽  
Logarithmic Correction ◽  
Square Root ◽  
Critical Systems ◽  
Intensive Study ◽  
Loop Contribution ◽  
Large N ◽  
Logarithmic Scaling

Motzkin and Fredkin spin chains exhibit the extraordinary amount of entanglement scaling as a square-root of the volume, which is beyond logarithmic scaling in the ordinary critical systems. Intensive study of such spin systems is urged to reveal novel features of quantum entanglement. As a study of the systems from a different viewpoint, we introduce large-N matrix models with so-called A B A B interactions, in which correlation functions reproduce the entanglement scaling in tree and planar Feynman diagrams. Including loop diagrams naturally defines an extension of the Motzkin and Fredkin spin chains. Contribution from the whole loop effects at large N gives the growth of the power of 3 / 2 (with logarithmic correction), further beyond the square-root scaling. The loop contribution provides fluctuating two-dimensional bulk geometry, and the enhancement of the entanglement is understood as an effect of quantum gravity.

scholarly journals CONSTRAINTS IN QUANTUM GEOMETRODYNAMICS

2004 ◽  
Vol 19 (10) ◽  
pp. 1609-1638 ◽  
Author(s):  
ADRIAN P. GENTLE ◽  
NATHAN D. GEORGE ◽  
ARKADY KHEYFETS ◽  
WARNER A. MILLER
Keyword(s):  
Quantum Gravity ◽  
General Setting ◽  
Square Root ◽  
Dynamical Equations ◽  
Dynamic Content ◽  
Quantization Formalism ◽  
Canonical Quantum Gravity ◽  
First Time ◽  
Quantum Geometrodynamics ◽  
Canonical Quantum

We compare different treatments of the constraints in canonical quantum gravity. The standard approach on the superspace of 3-geometries treats the constraints as the sole carriers of the dynamic content of the theory, thus rendering the traditional dynamical equations obsolete. Quantization of the constraints in both the Dirac and ADM square root Hamiltonian approaches leads to the well known problems of time evolution. These problems of time are of both an interpretational and technical nature. In contrast, the geometrodynamic quantization procedure on the superspace of the true dynamical variables separates the issues of quantization from the enforcement of the constraints. The resulting theory takes into account states that are off-shell with respect to the constraints, and thus avoids the problems of time. We develop, for the first time, the geometrodynamic quantization formalism in a general setting and show that it retains all essential features previously illustrated in the context of homogeneous cosmologies.

Large-N reduction in spin systems and Griffiths singularities

1983 ◽  
Vol 225 (4) ◽  
pp. 551-564 ◽  
Author(s):  
Marc Mezard
Keyword(s):  
Spin Systems ◽  
Large N

scholarly journals A logarithmic correction in the entropy functional formalism

2016 ◽  
Vol 25 (07) ◽  
pp. 1650080 ◽  
Author(s):  
Fayçal Hammad ◽  
Mir Faizal
Keyword(s):  
Quantum Gravity ◽  
Modified Gravity ◽  
Correction Term ◽  
Modified Theories Of Gravity ◽  
Logarithmic Correction ◽  
Functional Formalism ◽  
Entropy Formula ◽  
Entropy Functional ◽  
Modified Gravity Theories ◽  
Theories Of Gravity

The entropy functional formalism allows one to recover general relativity, modified gravity theories, as well as the Bekenstein–Hawking entropy formula. In most approaches to quantum gravity, the Bekenstein–Hawking’s entropy formula acquires a logarithmic correction term. As such terms occur almost universally in most approaches to quantum gravity, we analyze the effect of such terms on the entropy functional formalism. We demonstrate that the leading correction to the micro-canonical entropy in the entropy functional formalism can be used to recover modified theories of gravity already obtained with an uncorrected micro-canonical entropy. Furthermore, since the entropy functional formalism reproduces modified gravity, the rise of gravity-dependent logarithmic corrections turns out to be one way to impose constraints on these theories of modified gravity. The constraints found here for the simple case of an [Formula: see text]-gravity are the same as those obtained in the literature from cosmological considerations.

Effect of post-Newtonian-like self-energy, quantum gravity and exchange correlations on Schwarzschild black hole: Application of uncertainty principle

2020 ◽  
Vol 35 (11) ◽  
pp. 2050081
Author(s):  
Baljeet Kaur Lotte ◽  
Subodha Mishra
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Correlation Energy ◽  
Particle System ◽  
Gravitational Interaction ◽  
Schwarzschild Black Hole ◽  
Loop Contribution ◽  
Exchange Correlation ◽  
Self Energy ◽  
Energy Quantum

The expressions for the corrected radius and the Hawking temperature of a Schwarzschild black hole are derived by calculating the total energy of a self-gravitating system of N fermions when the corrections to gravitational interaction due to post-Newtonian-like self-energy due to two graviton exchange- and one-loop contribution of quantum gravity effect are included. Since the particles are fermions, the exchange-correlation energy is also included consistently. It is found that though the three corrections are small, the correction due to the exchange-correlation is much more than the other two. The configuration of the many-particle system that we study is possible since it has no Buchdahl limit in the post-Newtonian approximation.

scholarly journals RELAXING NEAR THE CRITICAL POINT

2001 ◽  
Vol 16 (supp01c) ◽  
pp. 1274-1276
Author(s):  
M. SIMIONATO
Keyword(s):  
Critical Point ◽  
Heavy Ions ◽  
Distribution Functions ◽  
Critical Systems ◽  
Chiral Phase ◽  
Long Wavelength ◽  
Equilibrium Dynamics ◽  
Slowing Down ◽  
Large N ◽  
Early Universe Cosmology

I present an analysis of the relaxation rate for long-wavelength fluctuations of the order parameter in an O(N) scalar theory near the critical point. Our motivation is to model the non-equilibrium dynamics of critical fluctuations near the chiral phase transition in QCD. In the next-to-leading order in the large N expansion we find a critical slowing down regime, i.e. an increasing of the relaxation time of long wavelengths fluctuations. This result suggests, for near critical systems, relevant deviations from thermal equilibrium for the distribution functions of low-energy particles and could have important phenomenological consequences in Heavy Ions Collision and in the Early Universe Cosmology.

scholarly journals Quantum gravity and spin systems

1995 ◽  
Vol 42 (1-3) ◽  
pp. 710-712 ◽  
Author(s):  
W. Beirl ◽  
P. Homolka ◽  
B. Krishnan ◽  
H. Markum ◽  
J. Riedler
Keyword(s):  
Quantum Gravity ◽  
Spin Systems

ONE AND QUASI-ONE DIMENSIONAL SPIN SYSTEMS

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2329-2336 ◽  
Author(s):  
Elisa Ercolessi
Keyword(s):  
Condensed Matter ◽  
Quantum Spin ◽  
Spin Systems ◽  
Spin Chains ◽  
Famous Conjecture ◽  
One Dimensional ◽  
Conformal Field ◽  
Quantum Spin Models ◽  
Low Dimensional ◽  
Antiferromagnetic Spin

Quantum spin models represent one of the most studied examples of application of low-dimensional field theories to condensed matter systems. In this paper we will review some chapters of this hystory, that dates back to the early '80, when Haldane put forward his by now famous conjecture on antiferromagnetic spin chains, and reaches the present days, with the most advanced applications of integrable models and conformal field theory.

scholarly journals Spin-spin correlation functions of spin systems coupled to 2-d quantum gravity for 0 < c < 1

1997 ◽  
Vol 53 (1-3) ◽  
pp. 725-727 ◽  
Author(s):  
J. Ambjørn ◽  
K.N. Anagnostopoulos ◽  
U. Magnea ◽  
G. Thorleifsson
Keyword(s):  
Quantum Gravity ◽  
Correlation Functions ◽  
Spin Correlation ◽  
Spin Systems
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