Chiral central charge from a single bulk wave function

Abstract

A $(2+1)$-dimensional gapped quantum many-body system can have a topologically protected energy current at its edge. The magnitude of this current is determined entirely by the temperature and the chiral central charge, a quantity associated with the effective field theory of the edge. We derive a formula for the chiral central charge that, akin to the topological entanglement entropy, is completely determined by the many-body ground state wave function in the bulk. According to our formula, nonzero chiral central charge gives rise to a topological obstruction that prevents the ground state wave function from being real-valued in any local product basis.

4+6 pages, 6 figures, added references, minor changes

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• Multipartitioning topological phases by vertex states and quantum entanglement
• From entanglement generated dynamics to the gravitational anomaly and chiral central charge
• A universal tripartite entanglement signature of ungappable edge states
• Modular Commutators in Conformal Field Theory
• Entanglement in tripartitions of topological orders: a diagrammatic approach
• Complete crystalline topological invariants from partial rotations in (2+1)D invertible fermionic states and Hofstadter's butterfly
• Extracting higher central charge from a single wave function
• Generalized Real-space Chern Number Formula and Entanglement Hamiltonian
• Multipartite entanglement in two-dimensional chiral topological liquids
• Multipartite edge modes and tensor networks
• Extracting topological orders of generalized Pauli stabilizer codes in two dimensions
• Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders
• Playing nonlocal games with phases of quantum matter
• Anyon Quantum Dimensions from an Arbitrary Ground State Wave Function
• Many-body systems with spurious modular commutators
• Edge Theories for Anyon Condensation Phase Transitions
• Conformal geometry from entanglement
• Detecting topological order from modular transformations of ground states on the torus
• Finite-Entanglement Scaling of 2D Metals
• Crystalline invariants of fractional Chern insulators
• Remote detectability from entanglement bootstrap I: Kirby's torus trick
• Entanglement Spectrum as a diagnostic of chirality of Topological Spin Liquids: Analysis of an $\mathrm{SU}(3)$ PEPS
• Most two-dimensional bosonic topological orders forbid sign-problem-free quantum Monte Carlo: Nonpositive Gauss sum as an indicator
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• (2+1)D topological phases with RT symmetry: many-body invariant, classification, and higher order edge modes
• Immersed figure-8 annuli and anyons
• Rényi-like entanglement probe of the chiral central charge
• Knots and entanglement
• Central Charge in Quantum Optics
• Geometric additivity of modular commutator for multipartite entanglement
• Detection of 2D SPT Order with Partial Symmetries
• Twisted quantum doubles are sign problem-free