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

Abstract

The stability and dynamics of almost strong zero and $\pi$ modes in weakly non-integrable 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. The structure of the perturbation theory and thus the lifetime of the modes is governed by the conservation of quasi-energy modulo $2\pi /T$, where $T$ is the period of the Floquet system. If the quasi-energies of minimally $4n-1$ quasi-particles adds up to zero (or $\pi /T$ for a $\pi$ mode), the lifetime is proportional to $1/J_z^{2n}$. 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.

References in corpus (10)

• Noise-resilient Edge Modes on a Chain of Superconducting Qubits
• Spin conductivity in almost integrable spin chains
• Floquet generation of Second Order Topological Superconductor
• Dynamics of almost strong edge modes in spin chains away from integrability
• Long-lived period-doubled edge modes of interacting and disorder-free Floquet spin chains
• Lower bounds for the conductivities of correlated quantum systems
• Dephasing enhanced strong Majorana zero modes in 2D and 3D higher-order topological superconductors
• Stability of Floquet Majorana box qubits
• Stochastic strong zero modes and their dynamical manifestations
• Non-integrable Floquet Ising model with duality twisted boundary conditions

Cited by in corpus (10)

• Strong zero modes in integrable quantum circuits
• Slowly decaying zero mode in a weakly non-integrable boundary impurity model
• A Universal Model of Floquet Operator Krylov Space
• Self-similar phase diagram of the Fibonacci-driven quantum Ising model
• Robust spectral $\pi$ pairing in the random-field Floquet quantum Ising model
• Disorder induced topological phase transition in a driven Majorana chain
• Duality defect in a deformed transverse-field Ising model
• Isolated zero mode in a quantum computer from a duality twist
• Engineering Hierarchical Symmetries
• Floquet Product Mode