Relating bulk to boundary entanglement

Abstract

Quantum many-body systems have a rich structure in the presence of boundaries. We study the groundstates of conformal field theories (CFTs) and Lifshitz field theories in the presence of a boundary through the lens of the entanglement entropy. For a family of theories in general dimensions, we relate the universal terms in the entanglement entropy of the bulk theory with the corresponding terms for the theory with a boundary. This relation imposes a condition on certain boundary central charges. For example, in $2+1$ dimensions, we show that the corner-induced logarithmic terms of free CFTs and certain Lifshitz theories are simply related to those that arise when the corner touches the boundary. We test our findings on the lattice, including a numerical implementation of Neumann boundary conditions. We also propose an ansatz, the boundary Extensive Mutual Information model, for a CFT with a boundary whose entanglement entropy is purely geometrical. This model shows the same bulk-boundary connection as Dirac fermions and certain supersymmetric CFTs that have a holographic dual. Finally, we discuss how our results can be generalized to all dimensions as well as to massive quantum field theories.

13+6 pages, 8+1 figures, 2+1 tables; v2: match published version

References in corpus (24)

• Holographic c-theorems in arbitrary dimensions
• Seeing a c-theorem with holography
• Topological Order and Conformal Quantum Critical Points
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Entanglement entropy, conformal invariance and extrinsic geometry
• Universal terms for the entanglement entropy in 2+1 dimensions
• Remarks on the entanglement entropy for disconnected regions
• Universality of corner entanglement in conformal field theories
• Boundary Conformal Field Theory and a Boundary Central Charge
• The g-theorem and quantum information theory
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Displacement Operators and Constraints on Boundary Central Charges
• Entanglement entropy for a Dirac fermion in three dimensions: vertex contribution
• Corner contribution to the entanglement entropy of strongly-interacting O(2) quantum critical systems in 2+1 dimensions
• Corner contributions to holographic entanglement entropy in AdS4/BCFT3
• Irreversibility in quantum field theories with boundaries
• Mutual information and the structure of entanglement in quantum field theory
• Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
• Entanglement entropy for even spheres
• Quantum spin chains with multiple dynamics
• Entanglement entropy for odd spheres
• Generalizing the entanglement entropy of singular regions in conformal field theories
• Entanglement Entropy and Mutual Information of Circular Entangling Surfaces in 2 + 1-dimensional Quantum Lifshitz Model
• On the entanglement across a cubic interface in 3+1 dimensions

Cited by in corpus (14)

• CFT in AdS and boundary RG flows
• Balanced Partial Entanglement and the Entanglement Wedge Cross Section
• Formulas for Partial Entanglement Entropy
• Logarithmic Negativity in Quantum Lifshitz Theories
• Entanglement of skeletal regions
• Massless Lifshitz Field Theory for Arbitrary $z$
• Geometric entanglement in integer quantum Hall states
• Entanglement entropies of an interval for the massless scalar field in the presence of a boundary
• On shape dependence of holographic entanglement entropy in AdS4/CFT3 with Lifshitz scaling and hyperscaling violation
• Note on anomalous currents for a free theory
• The entanglement entropy of the quantum Hall edge and its geometric contribution
• Geometric entanglement in integer quantum Hall states with boundaries
• Boundary-induced singularity in strongly-correlated quantum systems at finite temperature
• Channel induced dynamics of quantum information in mixed state free QFTs