Quantum geometry and $X$-wave magnets with $X=p,d,f,g,i$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918385744347136 |
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| author | Ezawa, Motohiko |
| author_facet | Ezawa, Motohiko |
| contents | Quantum geometry is a differential geometry based on quantum mechanics. It is related to various transport and optical properties in condensed matter physics. The Zeeman quantum geometry is a generalization of quantum geometry including the spin degrees of freedom. It is related to electromagnetic cross responses. Quantum geometry is generalized to non-Hermitian systems and density matrices. Especially, the latter is quantum information geometry, where the quantum Fisher information naturally arises as quantum metric. We apply these results to the $X$-wave magnets, which include $d$% -wave, $g$-wave and $i$-wave altermagnets as well as $p$-wave and $f$-wave magnets. They have universal physics for anomalous Hall conductivity, tunneling magneto-resistance and planar Hall effect. We also study magneto-optical conductivity, magnetic circular dichroism and Friedel oscillations in the $X$-wave magnets. Various analytic formulas are derived in the case of two-band Hamiltonians. This paper presents a review of recent progress together with some original results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_05477 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum geometry and $X$-wave magnets with $X=p,d,f,g,i$ Ezawa, Motohiko Mesoscale and Nanoscale Physics Materials Science Mathematical Physics Applied Physics Quantum Physics Quantum geometry is a differential geometry based on quantum mechanics. It is related to various transport and optical properties in condensed matter physics. The Zeeman quantum geometry is a generalization of quantum geometry including the spin degrees of freedom. It is related to electromagnetic cross responses. Quantum geometry is generalized to non-Hermitian systems and density matrices. Especially, the latter is quantum information geometry, where the quantum Fisher information naturally arises as quantum metric. We apply these results to the $X$-wave magnets, which include $d$% -wave, $g$-wave and $i$-wave altermagnets as well as $p$-wave and $f$-wave magnets. They have universal physics for anomalous Hall conductivity, tunneling magneto-resistance and planar Hall effect. We also study magneto-optical conductivity, magnetic circular dichroism and Friedel oscillations in the $X$-wave magnets. Various analytic formulas are derived in the case of two-band Hamiltonians. This paper presents a review of recent progress together with some original results. |
| title | Quantum geometry and $X$-wave magnets with $X=p,d,f,g,i$ |
| topic | Mesoscale and Nanoscale Physics Materials Science Mathematical Physics Applied Physics Quantum Physics |
| url | https://arxiv.org/abs/2512.05477 |