Rényi-like entanglement probe of the chiral central charge

• URL: http://arxiv.org/abs/2512.20608v1
• Date: Tue, 23 Dec 2025 18:55:34 GMT
• Title: Rényi-like entanglement probe of the chiral central charge
• Authors: Julian Gass, Michael Levin,
• Abstract summary: We propose a ground state entanglement probe for gapped, two-dimensional quantum many-body systems.<n>For integer values of $$ and $$, our quantity $_,$ can be expressed as an expectation value of permutation operators acting on an appropriate replica system.
• Score: 1.0742675209112622
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $ω_{α,β}$, is parameterized by two positive real numbers $α, β$, 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 $ω_{α,β}$ for gapped ground states of non-interacting fermion Hamiltonians as well as ground states of string-net models. In both cases, we find that $ω_{α,β}$ takes a universal value related to the chiral central charge. For integer values of $α$ and $β$, our quantity $ω_{α,β}$ can be expressed as an expectation value of permutation operators acting on an appropriate replica system, providing a natural route to measuring $ω_{α,β}$ in numerical simulations and potentially, experiments.

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