Identifying chiral topological order in microscopic spin models by modular commutator
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908579651387392 |
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| author | Maity, Avijit Kumar, Aman Tripathi, Vikram |
| author_facet | Maity, Avijit Kumar, Aman Tripathi, Vikram |
| contents | The chiral central charge $c_-$ is a key topological invariant of the edge characterizing the bulk two-dimensional chiral topological order, but its direct evaluation in microscopic spin models has long been a challenge, especially for non-abelian topological order. Building on the recently developed modular commutator formalism, we numerically obtain $c_-$ directly from single ground-state wave functions of two-dimensional interacting spin models that have chiral topological order. This provides a geometry-independent and bulk diagnostic of chirality. We study two nonintegrable systems -- the Zeeman-Kitaev honeycomb model and the kagome antiferromagnet -- both subjected to scalar spin chirality perturbations. We find that the modular commutator yields results consistent with the expected topological quantum field theories. We also compute the topological entanglement entropy which provides an independent diagnostic of the topological orders. Our work establishes modular commutators as a powerful numerical probe of chiral topological order in strongly correlated quantum magnets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06086 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Identifying chiral topological order in microscopic spin models by modular commutator Maity, Avijit Kumar, Aman Tripathi, Vikram Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics The chiral central charge $c_-$ is a key topological invariant of the edge characterizing the bulk two-dimensional chiral topological order, but its direct evaluation in microscopic spin models has long been a challenge, especially for non-abelian topological order. Building on the recently developed modular commutator formalism, we numerically obtain $c_-$ directly from single ground-state wave functions of two-dimensional interacting spin models that have chiral topological order. This provides a geometry-independent and bulk diagnostic of chirality. We study two nonintegrable systems -- the Zeeman-Kitaev honeycomb model and the kagome antiferromagnet -- both subjected to scalar spin chirality perturbations. We find that the modular commutator yields results consistent with the expected topological quantum field theories. We also compute the topological entanglement entropy which provides an independent diagnostic of the topological orders. Our work establishes modular commutators as a powerful numerical probe of chiral topological order in strongly correlated quantum magnets. |
| title | Identifying chiral topological order in microscopic spin models by modular commutator |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2510.06086 |