Decay rates of almost strong modes in Floquet spin chains beyond Fermi's Golden Rule

Journal Article · 04 August 2023 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.108.075112 · OSTI ID:1993576

Yeh, Hsiu-Chung ^[1]; Rosch, Achim ^[2]; Mitra, Aditi ^[3]

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1. New York University (NYU), NY (United States); New York University
2. University of Cologne (Germany)
3. New York University (NYU), NY (United States)

The stability and dynamics of almost strong zero and π modes in weakly nonintegrable Floquet spin chains are investigated. Such modes can also be viewed as localized Majorana modes at the edge of a topological superconductor. Perturbation theory in the strength of integrability breaking interaction J_z is employed to estimate the decay rates of these modes, and compared to decay rates obtained from exact diagonalization. Here, the structure of the perturbation theory and thus the lifetime of the modes is governed by the conservation of quasienergy modulo 2π/T, where T is the period of the Floquet system. If there are 4n – 1 bulk excitations whose quasienergies add up to zero (or π/T for a π mode), one obtains a decay channel of the Majorana mode with a decay rate proportional to $$J$$$^{2n}_{z}$$. Thus the lifetime is sensitively controlled by the width of the single-particle Floquet bands. For regimes where the decay rates are quadratic in J_z, an analytic expression for the decay rate in terms of an infinite temperature autocorrelation function of the integrable model is derived, and shown to agree well with exact diagonalization.

• Research Organization: New York University (NYU), NY (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0010821
• OSTI ID: 1993576
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 7 Vol. 108; ISSN 2469-9950
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English