From entanglement generated dynamics to the gravitational anomaly and chiral central charge

Abstract

We apply modular flow -- entanglement generated dynamics -- to characterize quantum orders of ground state wavefunctions. In particular, we study the linear response of the entanglement entropy of a simply connected region with respect to modular flow. First, we apply it to (1+1)D conformal field theories and demonstrate its relationship to the chiral central charge -- or equivalently the perturbative gravitational anomaly -- which is shown to vanish. Next, we apply it to (2+1)D gapped ground states where it reduces to a recently proposed formula by Kim et. al. that is conjectured to compute the edge chiral central charge. Modular flow provides an intuitive picture for this conjecture based on bulk-edge correspondence. We also provide numerics on free fermion models that lend support to our picture.

5 pages, 4 figures

References in corpus (6)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Towards a derivation of holographic entanglement entropy
• Physics at the entangling surface
• Chiral central charge from a single bulk wave function
• Modular commutator in gapped quantum many-body systems
• Modular Commutators in Conformal Field Theory

Cited by in corpus (17)

• A Noisy Approach to Intrinsically Mixed-State Topological Order
• Symmetry-enforced many-body separability transitions
• Modular Commutators in Conformal Field Theory
• AdS/BCFT from Conformal Bootstrap: Construction of Gravity with Branes and Particles
• Entanglement in tripartitions of topological orders: a diagrammatic approach
• Universal definition of the non-conformal trace anomaly
• Extracting higher central charge from a single wave function
• Generalized Real-space Chern Number Formula and Entanglement Hamiltonian
• Multi wavefunction overlap and multi entropy for topological ground states in (2+1) dimensions
• Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders
• Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories
• Anyon Quantum Dimensions from an Arbitrary Ground State Wave Function
• Many-body systems with spurious modular commutators
• Petz map recovery for long-range entangled quantum many-body states
• Rényi-like entanglement probe of the chiral central charge
• Higher Hall conductivity from a single wave function: Obstructions to symmetry-preserving gapped edge of (2+1)D topological order
• Geometric additivity of modular commutator for multipartite entanglement