Entanglement Entropy in Generalised Quantum Lifshitz Models

Abstract

We compute universal finite corrections to entanglement entropy for generalised quantum Lifshitz models in arbitrary odd spacetime dimensions. These are generalised free field theories with Lifshitz scaling symmetry, where the dynamical critical exponent $z$ equals the number of spatial dimensions $d$, and which generalise the 2+1-dimensional quantum Lifshitz model to higher dimensions. We analyse two cases: one where the spatial manifold is a $d$-dimensional sphere and the entanglement entropy is evaluated for a hemisphere, and another where a $d$-dimensional flat torus is divided into two cylinders. In both examples the finite universal terms in the entanglement entropy are scale invariant and depend on the compactification radius of the scalar field.

arXiv comment60 pages (including appendices), 5 figures; v2: references added, presentation improved, conclusions unchanged, v3: matching published version

References in corpus (70)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entanglement Entropy and Quantum Field Theory
• Area laws for the entanglement entropy - a review
• Aspects of Holographic Entanglement Entropy
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement entropy and conformal field theory
• The dS/CFT Correspondence
• Gravity Duals of Lifshitz-like Fixed Points
• On Geometric Entropy
• Quantum entanglement in condensed matter systems
• Entanglement entropy in free quantum field theory
• Topological Order and Conformal Quantum Critical Points
• Non-relativistic holography
• Holographic Entanglement Entropy
• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Entanglement entropy, conformal invariance and extrinsic geometry
• Entanglement entropy: holography and renormalization group
• F-Theorem without Supersymmetry
• Shannon and entanglement entropies of one- and two-dimensional critical wave functions
• Universality of corner entanglement in conformal field theories
• Distributional Geometry of Squashed Cones
• Universal entanglement entropy in 2D conformal quantum critical points
• Explicit formulas for GJMS-operators and $Q$-curvatures
• Multidimensional extension of the generalized Chowla-Selberg formula
• Corner contributions to holographic entanglement entropy
• Logarithmic terms in entanglement entropies of 2D quantum critical points and Shannon entropies of spin chains
• On Shape Dependence and RG Flow of Entanglement Entropy
• Scalar Field Theories with Polynomial Shift Symmetries
• Universal corner entanglement from twist operators
• Free box^k Scalar Conformal Field Theory
• Vacuum energy on orbifold factors of spheres
• Effective action in spherical domains
• Bounds on corner entanglement in quantum critical states
• Entanglement Evolution in Lifshitz-type Scalar Theories
• Entanglement Entropy in Lifshitz Theories
• Polyakov formulas for GJMS operators from AdS/CFT
• Boundary F-maximization
• Universal entanglement for higher dimensional cones
• Entanglement in gapless resonating valence bond states
• Two-cylinder entanglement entropy under a twist
• Heat kernel methods for Lifshitz theories
• Rényi entanglement entropies in quantum dimer models : from criticality to topological order
• Correlation functions in theories with Lifshitz scaling
• Exact results for corner contributions to the entanglement entropy and Renyi entropies of free bosons and fermions in 3d
• Entanglement Entropy for Singular Surfaces in Hyperscaling violating Theories
• Cascading Multicriticality in Nonrelativistic Spontaneous Symmetry Breaking
• Universal Behavior of Entanglement in 2D Quantum Critical Dimer Models
• On conformally covariant powers of the Laplacian
• Conformal Powers of the Laplacian via Stereographic Projection
• Scaling of entanglement in $2+1$-dimensional scale-invariant field theories
• Partition function of free conformal fields in 3-plet representation
• Boundary Conformal Field Theory and Entanglement Entropy in Two-Dimensional Quantum Lifshitz Critical Point
• Lifshitz entanglement entropy from holographic cMERA
• Entanglement Entropy and Mutual Information of Circular Entangling Surfaces in 2 + 1-dimensional Quantum Lifshitz Model
• Corner contributions to holographic entanglement entropy in non-conformal backgrounds
• Cornering gapless quantum states via their torus entanglement
• The asymptotics of the Laplacian on a manifold with boundary II
• Hidden global conformal symmetry without Virasoro extension in theory of elasticity
• Holographic torus entanglement and its RG flow
• Multiplicative anomaly and zeta factorization
• Entanglement Entropy of Local Operators in Quantum Lifshitz Theory
• Holographic Weyl anomaly for GJMS operators: one Laplacian to rule them all
• Laplacian operators and Q-curvature on conformally Einstein manifolds
• Scrambling in the Quantum Lifshitz Model
• Numerical evaluation of spherical GJMS determinants for even dimensions
• Juhl's Formulae for GJMS Operators and Q-Curvatures
• The boundary F-theorem for free fields
• Multiple Gamma Function and Its Application to Computation of Series
• A technical note on the calculation of GJMS (Rac and Di) operator determinants

Cited by in corpus (12)

• Logarithmic Negativity in Quantum Lifshitz Theories
• Entanglement of skeletal regions
• Massless Lifshitz Field Theory for Arbitrary $z$
• Towards a unitary, renormalizable and ultraviolet-complete quantum theory of gravity
• On shape dependence of holographic entanglement entropy in AdS4/CFT3 with Lifshitz scaling and hyperscaling violation
• Entanglement Entropy of Excited States in the Quantum Lifshitz Model
• Entanglement Entropy with Lifshitz Fermions
• Entanglement in Lifshitz Fermion Theories
• More on entanglement properties of $Li{f}_4^{(2)}\times S^1\times S^5$ spacetime with string excitations
• Measurement-Induced Entanglement in Conformal Field Theory
• Entanglement entropies of an interval in the free Schrödinger field theory at finite density
• Rényi entropy of single-character CFTs on the torus