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  • Letter
  • Open Access

Topological properties of single-particle states decaying into a continuum due to interaction

B. Hawashin1,2,*, J. Sirker2,†, and G. S. Uhrig1,‡

  • *Contact author: bilal.hawashin@tu-dortmund.de
  • †Contact author: sirker@physics.umanitoba.ca
  • ‡Contact author: goetz.uhrig@tu-dortmund.de
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Phys. Rev. Research 6, L042041 – Published 12 November, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L042041

Abstract

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 H0 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 Heff=H0(k⃗)+Σ(ω,k⃗) 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 Heff 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 But the bulk-boundary correspondence appears to be no longer valid and edge modes delocalize.

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Phys. Rev. Research 6, L042041– Published 12 November, 2024
  • Received 10 October 2023
  • Revised 26 July 2024
  • Accepted 16 October 2024
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