Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2611.00902

Quantum Mpemba effect of Z2 symmetry restoration in the Dicke model

Dongni Chen, Wei Xiong, Peng-Cheng Li, Yee Sin Ang, Ching Hua Lee, Yi Qin

quant-phSubmitted Oct 31, 2026• Announced Nov 3, 2026
arXivHTMLPDF

Abstract

We study a symmetry-restoration quantum Mpemba effect in the dissipative Dicke model as an example of a weakly $\mathbb Z_2$-symmetric open quantum system, where the full Liouvillian is parity covariant although individual quantum jumps connect the two Hilbert-space parity sectors. Using the entanglement-asymmetry (EA) diagnostic to monitor parity restoration, we compare coherent-product and cat-product initial states. Coherent-product states show conventional relaxation, with larger initial asymmetry decaying more slowly and no Mpemba crossing observed. Cat-product states, by contrast, can reverse this hierarchy over a finite region of initial-state space. This reversal is enabled by initial-state mode filtering: the cat-product superposition suppresses the contributions of the leading slow Liouvillian modes, allowing a more asymmetric state to restore parity through faster decay channels. Our results reveal that symmetry-restoration QME can arise even when parity is preserved only as a weak Liouvillian symmetry, with quantum jumps mixing the Hilbert-space parity sectors. The anomalous relaxation is governed by initial-state-dependent filtering of the leading slow Liouvillian modes, providing a mechanism for symmetry-restoration QME beyond strongly conserved symmetry sectors.

Related papers

Symmetry Restoration and Quantum Mpemba Effect in Symmetric Random Circuits

Shuo Liu, Hao-Kai Zhang, Shuai Yin +1 more

Entanglement asymmetry, which serves as a diagnostic tool for symmetry breaking and a proxy for thermalization, has recently been proposed and studied in the context of symmetry restoration for quantum many-body systems undergoing a quench. In this Letter, we investigate symmetry restoration in various symmetric random quantum circuits, particularly focusing on the U(1) symmetry case. In contrast to nonsymmetric random circuits where the U(1) symmetry of a small subsystem can always be restored at late times, we reveal that symmetry restoration can fail in U(1)-symmetric circuits for certain weak symmetry-broken initial states in finite-size systems. In the early-time dynamics, we observe an intriguing quantum Mpemba effect implying that symmetry is restored faster when the initial state is more asymmetric. Furthermore, we also investigate the entanglement asymmetry dynamics for SU(2) and Z_{2} symmetric circuits and identify the presence and absence of the quantum Mpemba effect for the corresponding symmetries, respectively. A unified understanding of these results is provided through the lens of quantum thermalization with conserved charges.

arXiv:2403.08459•Physical Review Letters•Oct 4, 2024•102 citations

Higher-order Symmetric Quantum Mpemba Effect in Fragmented Systems

Sreemayee Aditya, Sara Murciano, Xhek Turkeshi

A quantum system can restore a broken symmetry faster the more strongly it initially breaks it, an anomaly known as the quantum Mpemba effect. Whether this effect survives once conservation laws fragment the Hilbert space into exponentially many disconnected Krylov sectors has remained open. We address this question for circuits and Hamiltonians with simultaneous charge and dipole conservation, the paradigmatic setting for strong Hilbert-space fragmentation. Combining a replica tensor-network formulation for charge and dipole-conserving gates, which reaches the annealed Rényi-2 entanglement asymmetry up to $L=128$, with Hamiltonian simulations and an exactly solvable dissipative model, we uncover a higher-order symmetric quantum Mpemba effect: the charge and dipole asymmetries each display Mpemba-like crossings on parametrically distinct timescales. Resolving the state into frozen and active Krylov sectors reveals the mechanism: frozen fragments retain a finite asymmetry that obstructs full restoration, while active fragments host the relaxation responsible for the crossings. Fragmentation thus does not preclude the quantum Mpemba effect but reshapes it into frozen memory and active-fragment relaxation, providing a framework for the Mpemba phenomenology of higher-moment symmetries.

quant-pharXiv:2606.06653•Jun 8, 2026•0 citations

Symmetry structure dependent diagnostic of the Quantum Mpemba Effect

Tamizhselvan S, Manju C, Bijay Kumar Agarwalla +1 more

Understanding symmetry restoration in isolated quantum many-body systems is an important problem in nonequilibrium many-body quantum physics. Recent studies have shown that the quantum Mpemba effect can be characterized through entanglement asymmetry, where states with stronger initial symmetry breaking restore symmetry faster. However, it remains unclear whether conventional energy-based measures, such as the trace distance, capture the same phenomenon. We investigate this question in closed spin-$1/2$ quantum systems with different symmetries by analyzing the dynamics of symmetry-breaking initial states. Combining numerical simulations with an analytical decomposition of the trace distance into symmetry-coherence and residual contributions, we identify the conditions under which trace distance tracks entanglement asymmetry and reproduces the Mpemba--like behavior observed in it. For charge symmetry, the residual contribution is negligible, making the trace distance effectively governed by symmetry-sector coherences. In contrast, for permutation symmetry, a significant residual contribution leads to qualitatively different relaxation dynamics. Our results establish when conventional energy-based diagnostics reliably capture symmetry-restoration dynamics and clarify the distinct physical information encoded by entanglement asymmetry and trace distance.

quant-pharXiv:2609.10470•Sep 10, 2026•0 citations

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

Zijun Wei, Mingdi Xu, Yefeng Song +3 more

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 $λ=-2q$, 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.

quant-pharXiv:2605.20930•May 21, 2026•0 citations

The quantum Mpemba effect in symmetric random Clifford circuits

Shion Yamashika, Filiberto Ares, Pasquale Calabrese

The quantum Mpemba effect is the counterintuitive phenomenon whereby a quantum state initially farther from equilibrium relaxes faster than one initially closer to it. We demonstrate this effect in random Clifford circuits with a conserved $\mathrm{U}(1)$ charge, using the entanglement asymmetry to characterize relaxation through dynamical symmetry restoration. Exact numerical simulations show that an initially more asymmetric state can become locally more symmetric than an initially less asymmetric one. We explain this behavior by mapping the dynamics onto a charge-conserving quantum automaton, in which the decay of the entanglement asymmetry is controlled by the statistics of encounters between two particle species evolving according to a symmetric simple exclusion process. This mapping yields an analytic expression for the entanglement asymmetry and provides a simple microscopic mechanism for the quantum Mpemba effect: stronger initial symmetry breaking corresponds to a denser particle configuration, which enhances the frequency of particle encounters and thereby accelerates symmetry restoration.

cond-mat.stat-mechCross-listedarXiv:2609.17988•Sep 17, 2026•0 citations

Selective Quantum Mpemba Dynamics in Chaotic Spin Chains

Ri-Hua Zheng, Yang Xiao, Yu Wang +2 more

In a symmetry-restoration quantum Mpemba effect, an initial state with stronger local symmetry breaking can lose that memory faster than a state that starts closer to the symmetric manifold. We study how this local ordering reversal depends on the spatial profile of a longitudinal field in a clean U(1)-conserving spin chain, comparing spectral level statistics with crossings of the entanglement asymmetry for the same Hamiltonians. We find that Gaussian orthogonal ensemble (GOE)-like level statistics alone do not determine whether Mpemba crossings occur. Across field textures, GOE-like spectra can occur with or without entanglement-asymmetry crossings at the same field strength. In a near-staggered detuned field, the total charge-sector coherence reverses its ordering while the entanglement asymmetry retains its initial order. This contrast links the crossing response to the distribution of local charge-sector coherence and its entropic weighting in the reduced density matrix.

quant-pharXiv:2607.07081•Jul 9, 2026•0 citations
We study a symmetry-restoration quantum Mpemba effect in the dissipative Dicke model as an example of a weakly Z2\mathbb Z_2Z2​-symmetric open quantum system, where the full Liouvillian is parity covariant although individual quantum jumps connect the two Hilbert-space parity sectors. Using the entanglement-asymmetry (EA) diagnostic to monitor parity restoration, we compare coherent-product and cat-product initial states. Coherent-product states show conventional relaxation, with larger initial asymmetry decaying more slowly and no Mpemba crossing observed. Cat-product states, by contrast, can reverse this hierarchy over a finite region of initial-state space. This reversal is enabled by initial-state mode filtering: the cat-product superposition suppresses the contributions of the leading slow Liouvillian modes, allowing a more asymmetric state to restore parity through faster decay channels. Our results reveal that symmetry-restoration QME can arise even when parity is preserved only as a weak Liouvillian symmetry, with quantum jumps mixing the Hilbert-space parity sectors. The anomalous relaxation is governed by initial-state-dependent filtering of the leading slow Liouvillian modes, providing a mechanism for symmetry-restoration QME beyond strongly conserved symmetry sectors.
Entanglement asymmetry, which serves as a diagnostic tool for symmetry breaking and a proxy for thermalization, has recently been proposed and studied in the context of symmetry restoration for quantum many-body systems undergoing a quench. In this Letter, we investigate symmetry restoration in various symmetric random quantum circuits, particularly focusing on the U(1) symmetry case. In contrast to nonsymmetric random circuits where the U(1) symmetry of a small subsystem can always be restored at late times, we reveal that symmetry restoration can fail in U(1)-symmetric circuits for certain weak symmetry-broken initial states in finite-size systems. In the early-time dynamics, we observe an intriguing quantum Mpemba effect implying that symmetry is restored faster when the initial state is more asymmetric. Furthermore, we also investigate the entanglement asymmetry dynamics for SU(2) and Z_{2} symmetric circuits and identify the presence and absence of the quantum Mpemba effect for the corresponding symmetries, respectively. A unified understanding of these results is provided through the lens of quantum thermalization with conserved charges.
A quantum system can restore a broken symmetry faster the more strongly it initially breaks it, an anomaly known as the quantum Mpemba effect. Whether this effect survives once conservation laws fragment the Hilbert space into exponentially many disconnected Krylov sectors has remained open. We address this question for circuits and Hamiltonians with simultaneous charge and dipole conservation, the paradigmatic setting for strong Hilbert-space fragmentation. Combining a replica tensor-network formulation for charge and dipole-conserving gates, which reaches the annealed Rényi-2 entanglement asymmetry up to L=128L=128L=128, with Hamiltonian simulations and an exactly solvable dissipative model, we uncover a higher-order symmetric quantum Mpemba effect: the charge and dipole asymmetries each display Mpemba-like crossings on parametrically distinct timescales. Resolving the state into frozen and active Krylov sectors reveals the mechanism: frozen fragments retain a finite asymmetry that obstructs full restoration, while active fragments host the relaxation responsible for the crossings. Fragmentation thus does not preclude the quantum Mpemba effect but reshapes it into frozen memory and active-fragment relaxation, providing a framework for the Mpemba phenomenology of higher-moment symmetries.
Understanding symmetry restoration in isolated quantum many-body systems is an important problem in nonequilibrium many-body quantum physics. Recent studies have shown that the quantum Mpemba effect can be characterized through entanglement asymmetry, where states with stronger initial symmetry breaking restore symmetry faster. However, it remains unclear whether conventional energy-based measures, such as the trace distance, capture the same phenomenon. We investigate this question in closed spin-1/21/21/2 quantum systems with different symmetries by analyzing the dynamics of symmetry-breaking initial states. Combining numerical simulations with an analytical decomposition of the trace distance into symmetry-coherence and residual contributions, we identify the conditions under which trace distance tracks entanglement asymmetry and reproduces the Mpemba--like behavior observed in it. For charge symmetry, the residual contribution is negligible, making the trace distance effectively governed by symmetry-sector coherences. In contrast, for permutation symmetry, a significant residual contribution leads to qualitatively different relaxation dynamics. Our results establish when conventional energy-based diagnostics reliably capture symmetry-restoration dynamics and clarify the distinct physical information encoded by entanglement asymmetry and trace distance.
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)SU(2)SU(2) symmetry, whereas the full Liouvillian retains only the U(1)U(1)U(1) symmetry associated with total magnetization. This structure pins a family of spatially uniform zero-U(1)U(1)U(1)-charge left eigenoperators with exact eigenvalues λ=−2qλ=-2qλ=−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-SSS limit. Since higher-qqq components decay rapidly, the q=1q=1q=1 comb tooth controls the long-time dynamics and yields universal D(t)∼e−2tD(t)\sim e^{-2t}D(t)∼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)SU(2)SU(2) symmetry restores slow-mode overlap and suppresses this acceleration.
The quantum Mpemba effect is the counterintuitive phenomenon whereby a quantum state initially farther from equilibrium relaxes faster than one initially closer to it. We demonstrate this effect in random Clifford circuits with a conserved U(1)\mathrm{U}(1)U(1) charge, using the entanglement asymmetry to characterize relaxation through dynamical symmetry restoration. Exact numerical simulations show that an initially more asymmetric state can become locally more symmetric than an initially less asymmetric one. We explain this behavior by mapping the dynamics onto a charge-conserving quantum automaton, in which the decay of the entanglement asymmetry is controlled by the statistics of encounters between two particle species evolving according to a symmetric simple exclusion process. This mapping yields an analytic expression for the entanglement asymmetry and provides a simple microscopic mechanism for the quantum Mpemba effect: stronger initial symmetry breaking corresponds to a denser particle configuration, which enhances the frequency of particle encounters and thereby accelerates symmetry restoration.
In a symmetry-restoration quantum Mpemba effect, an initial state with stronger local symmetry breaking can lose that memory faster than a state that starts closer to the symmetric manifold. We study how this local ordering reversal depends on the spatial profile of a longitudinal field in a clean U(1)-conserving spin chain, comparing spectral level statistics with crossings of the entanglement asymmetry for the same Hamiltonians. We find that Gaussian orthogonal ensemble (GOE)-like level statistics alone do not determine whether Mpemba crossings occur. Across field textures, GOE-like spectra can occur with or without entanglement-asymmetry crossings at the same field strength. In a near-staggered detuned field, the total charge-sector coherence reverses its ordering while the entanglement asymmetry retains its initial order. This contrast links the crossing response to the distribution of local charge-sector coherence and its entropic weighting in the reduced density matrix.