Quantum geometric bounds in spinful systems with trivial band topology
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909833491382272 |
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| author | Jankowski, Wojciech J. Slager, Robert-Jan Lange, Gunnar F. |
| author_facet | Jankowski, Wojciech J. Slager, Robert-Jan Lange, Gunnar F. |
| contents | We derive quantum geometric bounds in spinful systems with spin topology characterized by a single $\mathbb{Z}$ index protected by a spin gap. Our bounds provide geometric conditions on the spin topology, distinct from the known quantum geometric bounds associated with Wilson loops and nontrivial band topologies. As a result, we obtain broader bounds in time-reversal symmetric systems with a nontrivial $\mathbb{Z}_2$ index and also bounds in systems with a trivial $\mathbb{Z}_2$ index, where the quantum metric should be otherwise unbounded. We benchmark these findings with first-principles calculations in elemental bismuth realizing a nontrivial even spin-Chern number. Moreover, we connect these bounds to optical responses and show their robustness in the presence of disorder within a real space marker formulation, demonstrating that spin-resolved quantum geometry is observable in realistic experimental settings of impure materials. Finally, we connect spin bounds to quantum Cramér-Rao bounds that are central to quantum metrology, showing that elemental Bi and other spin-topological phases hold promises for topological free fermion quantum sensors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16428 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum geometric bounds in spinful systems with trivial band topology Jankowski, Wojciech J. Slager, Robert-Jan Lange, Gunnar F. Mesoscale and Nanoscale Physics Materials Science Optics Quantum Physics We derive quantum geometric bounds in spinful systems with spin topology characterized by a single $\mathbb{Z}$ index protected by a spin gap. Our bounds provide geometric conditions on the spin topology, distinct from the known quantum geometric bounds associated with Wilson loops and nontrivial band topologies. As a result, we obtain broader bounds in time-reversal symmetric systems with a nontrivial $\mathbb{Z}_2$ index and also bounds in systems with a trivial $\mathbb{Z}_2$ index, where the quantum metric should be otherwise unbounded. We benchmark these findings with first-principles calculations in elemental bismuth realizing a nontrivial even spin-Chern number. Moreover, we connect these bounds to optical responses and show their robustness in the presence of disorder within a real space marker formulation, demonstrating that spin-resolved quantum geometry is observable in realistic experimental settings of impure materials. Finally, we connect spin bounds to quantum Cramér-Rao bounds that are central to quantum metrology, showing that elemental Bi and other spin-topological phases hold promises for topological free fermion quantum sensors. |
| title | Quantum geometric bounds in spinful systems with trivial band topology |
| topic | Mesoscale and Nanoscale Physics Materials Science Optics Quantum Physics |
| url | https://arxiv.org/abs/2501.16428 |