Rényi-like entanglement probe of the chiral central charge

Abstract

We propose a ground state entanglement probe for gapped, two-dimensional quantum many-body systems that involves taking powers of reduced density matrices in a particular geometric configuration. This quantity, which we denote by ${\omega }_{\alpha ,\beta }$, is parameterized by two positive real numbers $\alpha ,\beta$, and can be seen as a ``Rényi-like" generalization of the modular commutator -- another entanglement probe proposed as a way to compute the chiral central charge from a bulk wave function. We obtain analytic expressions for ${\omega }_{\alpha ,\beta }$ for gapped ground states of non-interacting fermion Hamiltonians as well as ground states of string-net models. In both cases, we find that ${\omega }_{\alpha ,\beta }$ takes a universal value related to the chiral central charge. For integer values of $\alpha$ and $\beta$, our quantity ${\omega }_{\alpha ,\beta }$ can be expressed as an expectation value of permutation operators acting on an appropriate replica system, providing a natural route to measuring ${\omega }_{\alpha ,\beta }$ in numerical simulations and potentially, experiments.

15 pages, 6 figures

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