Almost strong zero modes at finite temperature

Journal Article · Wed Jun 11 00:00:00 UTC 2025 · Physical Review Research

DOI: https://doi.org/10.1103/PhysRevResearch.7.023245 · OSTI ID:2569168

Tausendpfund, Niklas  ^[1]; Mitra, Aditi  ^[2]; Rizzi, Matteo  ^[1]

---

1. Forschungszentrum Juelich (Germany); Univ. of Cologne (Germany)
2. New York Univ. (NYU), NY (United States)

Interacting fermionic chains exhibit extended regions of topological degeneracy of their ground states as a result of the presence of Majorana or parafermionic zero modes localized at the edges. In the opposite limit of infinite temperature, the corresponding nonintegrable spin chains, obtained via generalized Jordan-Wigner mapping, are known to host so-called almost strong zero modes, which are long-lived with respect to any bulk excitations. Here we study the fairly unexplored territory that bridges these two extreme cases of zero and infinite temperature. We blend two established techniques for states, the Lanczos series expansion and a tensor network ansatz, uplifting them to the level of operator algebra. This allows us to efficiently simulate large system sizes for arbitrarily long timescales and to extract the temperature-dependent decay rates. We observe that for the Kitaev-Hubbard model, the decay rate of the edge mode depends exponentially on the inverse temperature 𝛽, and on an effective energy scale Δ_eff that is greater than the thermodynamic gap of the system Δ.

• Research Organization: New York Univ. (NYU), NY (United States)
• Sponsoring Organization: German Research Foundation (DFG) (DFG); USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0010821
• OSTI ID: 2569168
• Journal Information: Physical Review Research, Journal Name: Physical Review Research Journal Issue: 2 Vol. 7; ISSN 2643-1564
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English