Two-cylinder entanglement entropy under a twist

Abstract

We study the von Neumann and Rényi entanglement entropy (EE) of scale-invariant theories defined on tori in 2+1 and 3+1 spacetime dimensions. We focus on spatial bi-partitions of the torus into two cylinders, and allow for twisted boundary conditions along the non-contractible cycles. Various analytical and numerical results are obtained for the universal EE of the relativistic boson and Dirac fermion conformal field theories (CFTs), and for the fermionic quadratic band touching and the boson with $z=2$ Lifshitz scaling. The shape dependence of the EE clearly distinguishes these theories, although intriguing similarities are found in certain limits. We also study the evolution of the EE when a mass is introduced to detune the system from its scale-invariant point, by employing a renormalized EE that goes beyond a naive subtraction of the area law. In certain cases we find non-monotonic behavior of the torus EE under RG flow, which distinguishes it from the EE of a disk.

47 pages, 13 figures

References in corpus (20)

• Towards a derivation of holographic entanglement entropy
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• 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
• Remarks on the entanglement entropy for disconnected regions
• Entanglement Entropy in the O(N) model
• Universality of corner entanglement in conformal field theories
• Universal entanglement entropy in 2D conformal quantum critical points
• Bulk Emergence and the RG Flow of Entanglement Entropy
• On bipartite Rokhsar-Kivelson points and Cantor deconfinement
• Entanglement Entropy in Critical Phenomena and Analogue Models of Quantum Gravity
• Corner contribution to the entanglement entropy of strongly-interacting O(2) quantum critical systems in 2+1 dimensions
• Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
• Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice
• Boundary Conformal Field Theory and Entanglement Entropy in Two-Dimensional Quantum Lifshitz Critical Point
• Holographic torus entanglement and its RG flow
• The Aharonov-Bohm Effect on Entanglement Entropy in Conformal Field Theory
• Shape dependence of two-cylinder Renyi entropies for free bosons on a lattice

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• Structure of Quantum Entanglement at a Finite Temperature Critical Point
• Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation
• Extracting subleading corrections in entanglement entropy at quantum phase transitions
• Relating bulk to boundary entanglement
• Entanglement Entropy in Generalised Quantum Lifshitz Models
• Lifshitz entanglement entropy from holographic cMERA
• Universal signatures of Dirac fermions in entanglement and charge fluctuations
• Entanglement of skeletal regions
• Geometric entanglement in integer quantum Hall states
• The Aharonov-Bohm Effect on Entanglement Entropy in Conformal Field Theory
• Entanglement Entropy with Lifshitz Fermions
• Entanglement in Lifshitz Fermion Theories
• The entanglement entropy of the quantum Hall edge and its geometric contribution
• Geometric entanglement in integer quantum Hall states with boundaries
• Universal divergence of the Renyi entropy of a thinly sliced torus at the Ising fixed point
• Enhanced area law in the Widom-Sobolev formula for the free Dirac operator in arbitrary dimension
• Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries
• Rényi entropies for one-dimensional quantum systems with mixed boundary conditions
• Holographic entanglement renormalisation for fermionic quantum matter