Connecting the Many-Body Chern Number to Luttinger's Theorem through Středa's Formula
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916079213740032 |
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| author | Gavensky, Lucila Peralta Sachdev, Subir Goldman, Nathan |
| author_facet | Gavensky, Lucila Peralta Sachdev, Subir Goldman, Nathan |
| contents | Relating the quantized Hall response of correlated insulators to many-body topological invariants is a key challenge in topological quantum matter. Here, we use Streda's formula to derive an expression for the many-body Chern number in terms of the single-particle interacting Green's function and its derivative with respect to a magnetic field. In this approach, we find that this many-body topological invariant can be decomposed in terms of two contributions, $N_3[G] + ΔN_3[G]$, where $N_3[G]$ is known as the Ishikawa-Matsuyama invariant and where the second term involves derivatives of Green's function and the self energy with respect to the magnetic perturbation. As a by-product, the invariant $N_3[G]$ is shown to stem from the derivative of Luttinger's theorem with respect to the probe magnetic field. These results reveal under which conditions the quantized Hall conductivity of correlated topological insulators is solely dictated by the invariant $N_3[G]$, providing new insight on the origin of fractionalization in strongly-correlated topological phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02483 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Connecting the Many-Body Chern Number to Luttinger's Theorem through Středa's Formula Gavensky, Lucila Peralta Sachdev, Subir Goldman, Nathan Strongly Correlated Electrons Mesoscale and Nanoscale Physics Relating the quantized Hall response of correlated insulators to many-body topological invariants is a key challenge in topological quantum matter. Here, we use Streda's formula to derive an expression for the many-body Chern number in terms of the single-particle interacting Green's function and its derivative with respect to a magnetic field. In this approach, we find that this many-body topological invariant can be decomposed in terms of two contributions, $N_3[G] + ΔN_3[G]$, where $N_3[G]$ is known as the Ishikawa-Matsuyama invariant and where the second term involves derivatives of Green's function and the self energy with respect to the magnetic perturbation. As a by-product, the invariant $N_3[G]$ is shown to stem from the derivative of Luttinger's theorem with respect to the probe magnetic field. These results reveal under which conditions the quantized Hall conductivity of correlated topological insulators is solely dictated by the invariant $N_3[G]$, providing new insight on the origin of fractionalization in strongly-correlated topological phases. |
| title | Connecting the Many-Body Chern Number to Luttinger's Theorem through Středa's Formula |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2309.02483 |