تقرير
Anomalous symmetries of quantum spin chains and a generalization of the Lieb-Schultz-Mattis theorem
| العنوان: | Anomalous symmetries of quantum spin chains and a generalization of the Lieb-Schultz-Mattis theorem |
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| المؤلفون: | Kapustin, Anton, Sopenko, Nikita |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Condensed Matter High Energy Physics - Theory Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics, Condensed Matter - Strongly Correlated Electrons, High Energy Physics - Theory |
| الوصف: | For any locality-preserving action of a group $G$ on a quantum spin chain one can define an anomaly index taking values in the group cohomology of $G$. The anomaly index is a kinematic quantity, it does not depend on the Hamiltonian. We prove that a nonzero anomaly index prohibits any $G$-invariant Hamiltonian from having $G$-invariant gapped ground states. Lieb-Schultz-Mattis-type theorems are a special case of this result when $G$ involves translations. In the case when the symmetry group $G$ is a Lie group, we define an anomaly index which takes values in the differentiable group cohomology as defined by J.-L. Brylinski and prove a similar result. Comment: 41 pages, 3 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.02533 |
| رقم الأكسشن: | edsarx.2401.02533 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |