Rényi-like entanglement probe of the chiral central charge
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911544233689088 |
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| author | Gass, Julian Levin, Michael |
| author_facet | Gass, Julian Levin, Michael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20608 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rényi-like entanglement probe of the chiral central charge Gass, Julian Levin, Michael Strongly Correlated Electrons Quantum Physics 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. |
| title | Rényi-like entanglement probe of the chiral central charge |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2512.20608 |