Geometric additivity of modular commutator for multipartite entanglement

Abstract

A recent surge of research in many-body quantum entanglement has uncovered intriguing properties of quantum many-body systems. A prime example is the modular commutator, which can extract a topological invariant from a single wave function. Here, we unveil novel geometric properties of many-body entanglement via a modular commutator of two-dimensional gapped quantum many-body systems. We obtain the geometric additivity of a modular commutator, indicating that modular commutator for a multipartite system may be an integer multiple of the one for tripartite systems. Using our additivity formula, we also derive a curious identity for the modular commutators involving disconnected intervals in a certain class of conformal field theories. We further illustrate this geometric additivity for both bulk and edge subsystems using numerical calculations of the Haldane and $\pi$-flux models.

4+8 pages, 6+10 figures, v2: updated references

References in corpus (11)

• Entanglement hamiltonians in two-dimensional conformal field theory
• Universal tripartite entanglement in one-dimensional many-body systems
• Chiral central charge from a single bulk wave function
• Modular commutator in gapped quantum many-body systems
• 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
• Extracting higher central charge from a single wave function
• Generalized Real-space Chern Number Formula and Entanglement Hamiltonian
• Anyon Quantum Dimensions from an Arbitrary Ground State Wave Function
• Many-body systems with spurious modular commutators