Chiral Central Charge from Real-Space Twist Operator Correlator
Abstract
Recent years have witnessed substantial progress in the entanglement-based characterization of quantum phases of matter, with growing interest in real-space formulas due to their theoretical and experimental relevance. For two-dimensional gapped quantum systems, we propose a universal real-space formula for the chiral central charge based on the twist-operator correlator Zg,h=⟨ψ(N)rvert𝒯A(g)𝒯B(h)𝒯C(g)𝒯C(h)lvertψ(N)⟩, where lvertψ(N)⟩=lvertψ⟩⊗ N is the N-copy state and g,h∈ SN are permutations. The twist operator 𝒯R(g) permutes the N replicas within region R according to g. For pairs (g,h) satisfying the spherical condition, we show that the phase of the correlator is determined by the chiral central charge c− through Zg,h/lvert Zg,hrvert=(θgθh/θgh)c−, where θgc− is the topological spin of the twist defect labeled by g∈ SN. The construction applies to both bosonic and fermionic systems. We derive the formula within a field-theoretic framework under suitable assumptions and further test it numerically in microscopic lattice models. Our results establish a universal connection between real-space entanglement structures and the chiral central charge, providing a systematic framework for characterizing chiral topological phases directly on the lattice.
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BibTeX
@misc{zang2026chiral,
title = {{Chiral Central Charge from Real-Space Twist Operator Correlator}},
author = {Yunlong Zang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08788},
eprint = {2610.08788},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08788},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Chiral Central Charge from Real-Space Twist Operator Correlator
AU - Yunlong Zang
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08788
UR - https://arxiv.org/abs/2610.08788
AB - Recent years have witnessed substantial progress in the entanglement-based characterization of quantum phases of matter, with growing interest in real-space formulas due to their theoretical and experimental relevance. For two-dimensional gapped quantum systems, we propose a universal real-space formula for the chiral central charge based on the twist-operator correlator Z_g,h=⟨ψ^(N)rvert𝒯_A(g)𝒯_B(h)𝒯_C(g)𝒯_C(h)lvertψ^(N)⟩, where lvertψ^(N)⟩=lvertψ⟩^⊗ N is the N-copy state and g,h∈ S_N are permutations. The twist operator 𝒯_R(g) permutes the N replicas within region R according to g. For pairs (g,h) satisfying the spherical condition, we show that the phase of the correlator is determined by the chiral central charge c_− through Z_g,h/lvert Z_g,hrvert=(θ_gθ_h/θ_gh)^c_−, where θ_g^c_− is the topological spin of the twist defect labeled by g∈ S_N. The construction applies to both bosonic and fermionic systems. We derive the formula within a field-theoretic framework under suitable assumptions and further test it numerically in microscopic lattice models. Our results establish a universal connection between real-space entanglement structures and the chiral central charge, providing a systematic framework for characterizing chiral topological phases directly on the lattice.
ER -