تقرير
Local Noether theorem for quantum lattice systems and topological invariants of gapped states
| العنوان: | Local Noether theorem for quantum lattice systems and topological invariants of gapped states |
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| المؤلفون: | Kapustin, Anton, Sopenko, Nikita |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Condensed Matter Mathematical Physics Quantum Physics |
| مصطلحات موضوعية: | Mathematical Physics, Condensed Matter - Statistical Mechanics, Condensed Matter - Strongly Correlated Electrons, Quantum Physics |
| الوصف: | We study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed (d+2)-form on the parameter space which generalizes the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. When the family is equivariant under the action of a compact Lie group G, topological invariants take values in the equivariant cohomology of the parameter space. These invariants unify and generalize the Hall conductance and the Thouless pump. A key role in these constructions is played by a certain differential graded Frechet-Lie algebra attached to any quantum lattice system. As a by-product, we describe ambiguities in charge densities and conserved currents for arbitrary lattice systems with rapidly decaying interactions. Comment: v2: exposition improved, minor errors corrected. Version to appear in Journal of Mathematical Physics. v3: missing pictures added |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1063/5.0085964 |
| URL الوصول: | http://arxiv.org/abs/2201.01327 |
| رقم الأكسشن: | edsarx.2201.01327 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1063/5.0085964 |
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