Symmetry-Induced Relaxation Comb and Strong Quantum Mpemba Effect in Long-Range XXZ Spin Chains

arXiv:2605.20930v4 Announce Type: replace Abstract: We uncover a symmetry-filtered mechanism for anomalous dissipative relaxation in a long-range XXZ spin chain subject to local dephasing. At the isotropic point, the coherent Hamiltonian has global $SU(2)$ symmetry, whereas the full Liouvillian retains only the $U(1)$ symmetry associated with total magnetization. This structure pins a family of spatially uniform zero-$U(1)$-charge left eigenoperators with exact eigenvalues $\lambda=-2q$, forming a Liouvillian relaxation comb. For the ferromagnetic Dicke ground state, the overlap envelope on this comb is known exactly at finite size and becomes Gaussian in the large-$S$ limit. Since higher-$q$ components decay rapidly, the $q=1$ comb tooth controls the long-time dynamics and yields universal $D(t)\sim e^{-2t}$ relaxation independent of system size and interaction range. This mode-accessibility filtering realizes a spectral strong quantum Mpemba effect: an initially farther state relaxes faster than closer thermal states because slow non-steady Liouvillian modes are inaccessible. Weak breaking of the Hamiltonian $SU(2)$ symmetry restores slow-mode overlap and suppresses this acceleration.

Abstract:We uncover a symmetry-filtered mechanism for anomalous dissipative relaxation in a long-range XXZ spin chain subject to local dephasing. At the isotropic point, the coherent Hamiltonian has global $SU(2)$ symmetry, whereas the full Liouvillian retains only the $U(1)$ symmetry associated with total magnetization. This structure pins a family of spatially uniform zero-$U(1)$-charge left eigenoperators with exact eigenvalues $\lambda=-2q$, forming a Liouvillian relaxation comb. For the ferromagnetic Dicke ground state, the overlap envelope on this comb is known exactly at finite size and becomes Gaussian in the large-$S$ limit. Since higher-$q$ components decay rapidly, the $q=1$ comb tooth controls the long-time dynamics and yields universal $D(t)\sim e^{-2t}$ relaxation independent of system size and interaction range. This mode-accessibility filtering realizes a spectral strong quantum Mpemba effect: an initially farther state relaxes faster than closer thermal states because slow non-steady Liouvillian modes are inaccessible. Weak breaking of the Hamiltonian $SU(2)$ symmetry restores slow-mode overlap and suppresses this acceleration.

Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas)

arXiv:2605.20930 [quant-ph]

(or arXiv:2605.20930v4 [quant-ph] for this version)

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Symmetry-Induced Relaxation Comb and Strong Quantum Mpemba Effect in Long-Range XXZ Spin Chains

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