Topological Properties of Single-Particle States Decaying into a Continuum due to Interaction
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| author | Hawashin, B. Sirker, J. Uhrig, G. S. |
| author_facet | Hawashin, B. Sirker, J. Uhrig, G. S. |
| contents | We investigate how topological Chern numbers can be defined when single-particle states hybridize with continua. We do so exemplarily in a bosonic Haldane model at zero temperature with an additional on-site decay of one boson into two and the conjugate fusion of two bosons into one. Restricting the Hilbert space to two bosons at maximum, the exact self-energy is accessible. We use the bilinear Hamiltonian $H_0$ corrected by the self-energy $Σ$ to compute Chern numbers by two different approaches. The results are gauged against a full many-body calculation in the Hilbert space where possible. We establish numerically and analytically that the effective Hamiltonian $H_\text{eff}=H_0(\vec k) +Σ(ω,\vec k)$ reproduces the correct many-body topology if the considered band does not overlap with the continuum. In case of overlaps, one can extend the definition of the Chern number to the non-Hermitian $H_\text{eff}$ and there is evidence that the Chern number changes at exceptional points. But the bulk-boundary correspondence appears to be no longer valid and edge modes delocalize. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_09957 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topological Properties of Single-Particle States Decaying into a Continuum due to Interaction Hawashin, B. Sirker, J. Uhrig, G. S. Mesoscale and Nanoscale Physics Other Condensed Matter Quantum Gases Strongly Correlated Electrons We investigate how topological Chern numbers can be defined when single-particle states hybridize with continua. We do so exemplarily in a bosonic Haldane model at zero temperature with an additional on-site decay of one boson into two and the conjugate fusion of two bosons into one. Restricting the Hilbert space to two bosons at maximum, the exact self-energy is accessible. We use the bilinear Hamiltonian $H_0$ corrected by the self-energy $Σ$ to compute Chern numbers by two different approaches. The results are gauged against a full many-body calculation in the Hilbert space where possible. We establish numerically and analytically that the effective Hamiltonian $H_\text{eff}=H_0(\vec k) +Σ(ω,\vec k)$ reproduces the correct many-body topology if the considered band does not overlap with the continuum. In case of overlaps, one can extend the definition of the Chern number to the non-Hermitian $H_\text{eff}$ and there is evidence that the Chern number changes at exceptional points. But the bulk-boundary correspondence appears to be no longer valid and edge modes delocalize. |
| title | Topological Properties of Single-Particle States Decaying into a Continuum due to Interaction |
| topic | Mesoscale and Nanoscale Physics Other Condensed Matter Quantum Gases Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2310.09957 |