Quantum Mpemba effect in long-range spin systems

One of the manifestations of the quantum Mpemba effect (QME) is that a tilted ferromagnet exhibits faster restoration of the spin-rotational symmetry after a quantum quench when starting from a larger tilt angle. This phenomenon has recently been observed experimentally in an ion trap that simulates a long-range spin chain. However, the underlying mechanism of the QME in the presence of long-range interactions remains unclear. Using the time-dependent spin-wave theory, we investigate the dynamical restoration of the spin-rotational symmetry and the QME in generic long-range spin systems. We show that quantum fluctuations of the magnetization drive the restoration of symmetry by melting the initial ferromagnetic order and are responsible for the QME. We find that this effect occurs across a wide parameter range in long-range systems, in contrast to its absence in some short-range counterparts.

💡 Research Summary

The paper provides a comprehensive theoretical explanation for the quantum Mpemba effect (QME) observed in recent ion‑trap experiments that simulate long‑range interacting spin chains. The authors consider a generic U(1)‑symmetric spin‑½ Hamiltonian with power‑law couplings J(r)∝|r|^{‑α} and an external longitudinal field h. The system is initialized in a tilted ferromagnetic product state |TF(θ,ϕ)⟩, which breaks the global spin‑rotation symmetry around the z‑axis for any polar angle 0<θ<π. After a sudden quench to the interacting Hamiltonian, the state evolves unitarily and the broken symmetry is gradually restored in subsystems.

To capture the dynamics, the authors employ time‑dependent spin‑wave theory. They move to a rotating frame where the instantaneous total magnetization ⟨M(t)⟩ points along the z‑axis, and then apply a Holstein‑Primakoff transformation to express spin operators in terms of bosonic operators b_i. Keeping terms up to quadratic order yields an effective Hamiltonian H̃ that describes non‑interacting Bogoliubov spin‑wave modes with dispersion ω_k=√(ξ_k²‑κ_k²), where ξ_k and κ_k depend on the interaction profile, anisotropy Δ, and the tilt angle θ. Stability of the spin‑wave expansion requires Im