The geometry and entanglement entropy of surfaces in loop quantum gravity
arXiv:1806.05937 · doi:10.1103/PhysRevD.98.066009
Abstract
In loop quantum gravity, the area element of embedded spatial surfaces is given by a well-defined operator. We further characterize the quantized geometry of such surfaces by proposing definitions for operators quantizing scalar curvature and mean curvature. By investigating their properties, we shed light on the nature of the geometry of surfaces in loop quantum gravity. We also investigate the entanglement entropy across surfaces in the case where spin network edges are running within the surface. We observe that, on a certain class of states, the entropy gradient across a surface is proportional to the mean curvature. In particular, the entanglement entropy is constant for small deformations of a minimal surface in this case.
References in corpus (28)
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Background Independent Quantum Gravity: A Status Report
- Discreteness of area and volume in quantum gravity
- Cool horizons for entangled black holes
- Quantum Geometry and Black Hole Entropy
- Quantum Theory of Gravity I: Area Operators
- Quantum Spin Dynamics (QSD)
- Black Hole Entropy from Loop Quantum Gravity
- Dust as a Standard of Space and Time in Canonical Quantum Gravity
- Black hole entropy from Quantum Geometry
- Linking Topological Quantum Field Theory and Nonperturbative Quantum Gravity
- Quantum Spin Dynamics (QSD) II
- Polyhedra in loop quantum gravity
- Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons
- A length operator for canonical quantum gravity
- Algebraic Quantum Gravity (AQG) IV. Reduced Phase Space Quantisation of Loop Quantum Gravity
- Scalar Material Reference Systems and Loop Quantum Gravity
- The length operator in Loop Quantum Gravity
- Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators
- Are the spectra of geometrical operators in Loop Quantum Gravity really discrete?
- Entanglement Entropy in Loop Quantum Gravity
- Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity II
- Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity I
- Discreteness of the volume of space from Bohr-Sommerfeld quantization
- New length operator for loop quantum gravity
- Gluing polyhedra with entanglement in loop quantum gravity
- A curvature operator for LQG
- The status of Quantum Geometry in the dynamical sector of Loop Quantum Cosmology