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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.10418 |
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| _version_ | 1866914184207269888 |
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| author | Ruba, Błażej Yang, Bowen |
| author_facet | Ruba, Błażej Yang, Bowen |
| contents | We establish a bulk--boundary correspondence for translation-invariant stabilizer states in arbitrary spatial dimension, formulated in the framework of modules over Laurent polynomial rings. To each stabilizer state restricted to half-space geometry we associate a boundary operator module. Boundary operator modules provide examples of quasi-symplectic modules, which are objects of independent mathematical interest. In their study, we use ideas from algebraic L-theory in a setting involving non-projective modules and non-unimodular forms. Our results about quasi-symplectic modules in one spatial dimension allow us to resolve the conjecture that every stabilizer state in two dimensions is characterized by a corresponding abelian anyon model with gappable boundary. Our techniques are also applicable beyond two dimensions, such as in the study of fractons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10418 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Witt Groups and Bulk-Boundary Correspondence for Stabilizer States Ruba, Błażej Yang, Bowen Mathematical Physics Strongly Correlated Electrons Commutative Algebra Quantum Physics We establish a bulk--boundary correspondence for translation-invariant stabilizer states in arbitrary spatial dimension, formulated in the framework of modules over Laurent polynomial rings. To each stabilizer state restricted to half-space geometry we associate a boundary operator module. Boundary operator modules provide examples of quasi-symplectic modules, which are objects of independent mathematical interest. In their study, we use ideas from algebraic L-theory in a setting involving non-projective modules and non-unimodular forms. Our results about quasi-symplectic modules in one spatial dimension allow us to resolve the conjecture that every stabilizer state in two dimensions is characterized by a corresponding abelian anyon model with gappable boundary. Our techniques are also applicable beyond two dimensions, such as in the study of fractons. |
| title | Witt Groups and Bulk-Boundary Correspondence for Stabilizer States |
| topic | Mathematical Physics Strongly Correlated Electrons Commutative Algebra Quantum Physics |
| url | https://arxiv.org/abs/2509.10418 |