Left-Right Entanglement Entropy of Boundary States

Abstract

We study entanglement entropy of boundary states in a free bosonic conformal field theory. A boundary state can be thought of as composed of a particular combination of left and right-moving modes of the two-dimensional conformal field theory. We investigate the reduced density matrix obtained by tracing over the right-moving modes in various boundary states. We consider Dirichlet and Neumann boundary states of a free noncompact as well as a compact boson. The results for the entanglement entropy indicate that the reduced system can be viewed as a thermal CFT gas. Our findings are in agreement and generalize results in quantum mechanics and quantum field theory where coherent states can also be considered. In the compact case we verify that the entanglement entropy expressions are consistent with T-duality.

arXiv comment15 pages, no figures. v2 References added, typos fixed

References in corpus (18)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Aspects of Holographic Entanglement Entropy
• Entropy and Area
• Time-dependence of correlation functions following a quantum quench
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Relative Entropy and Holography
• Thermodynamical Property of Entanglement Entropy for Excited States
• Entanglement Temperature and Entanglement Entropy of Excited States
• Entanglement of low-energy excitations in Conformal Field Theory
• Quantum Entanglement of Local Operators in Conformal Field Theories
• Entanglement in solvable many-particle models
• Thermalization and Revivals after a Quantum Quench in Conformal Field Theory
• Universal entanglement entropy in 2D conformal quantum critical points
• Notes on Quantum Entanglement of Local Operators
• Measuring Black Hole Formations by Entanglement Entropy via Coarse-Graining
• Entanglement Entropies in Conformal Systems with Boundaries
• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• Is entanglement entropy proportional to area?

Cited by in corpus (30)

• Tensionless Strings from Worldsheet Symmetries
• Edge theory approach to topological entanglement entropy, mutual information and entanglement negativity in Chern-Simons theories
• Universal features of left-right entanglement entropy
• Entanglement constant for conformal families
• Topological pseudo entropy
• Comments on Entanglement Entropy in String Theory
• Entanglement entropy at CFT junctions
• Entanglement and topological interfaces
• Universal relations for holographic interfaces
• Entanglement evolution across a conformal interface
• Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy
• Chiral entanglement in massive quantum field theories in 1+1 dimensions
• A note on entanglement entropy for topological interfaces in RCFTs
• Universal entanglement spectra in critical spin chains
• Entanglement asymmetry and symmetry defects in boundary conformal field theory
• Momentum-space entanglement and Loschmidt echo in Luttinger liquids after a quantum quench
• Momentum-space entanglement after a quench in one-dimensional disordered fermionic systems
• LREE of an Unstable Dressed-Dynamical D$p$-brane: Superstring Calculations
• Momentum-Space Entanglement in Heisenberg Spin-Half Ladders
• Geometry of the parameter space of a quantum system: Classical point of view
• Replica trick and string winding
• Left/right entanglement and thermalization of time dependent plane wave Green-Schwarz superstring
• Momentum-space entanglement after smooth quenches
• Distilling momentum-space entanglement in Luttinger liquids at finite temperature
• On the topological and crosscap entropies in non-oriented RCFTs
• Left-Right Entanglement Entropy for a Dp-brane with Dynamics and Background Fields
• Monstrous entanglement
• Effective thermodynamics of isolated entangled squeezed and coherent states
• Entanglement in a Maxwell Theory coupled to a non-relativistic particle
• LREE of a Dressed D$p$-brane with Transverse Motion in the Partially Compact Spacetime