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This study identifies a symmetry-filtered mechanism in long-range XXZ spin chains that generates a spectral strong quantum Mpemba effect, where distant states relax faster than closer thermal ones due to inaccessible slow modes. The research demonstrates how global SU(2) symmetry pinning specific Liouvillian eigenoperators creates universal relaxation dynamics independent of system size or interaction range. Weak breaking of this Hamiltonian symmetry restores standard overlap and suppresses the anomalous acceleration, offering precise control over dissipative pathways in quantum many-body systems.
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)
Full text under the publisher's open licence · 169 words
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