Higher-order Symmetric Quantum Mpemba Effect in Fragmented Systems

The quantum Mpemba effect (QME) describes a scenario where a quantum system that is initially further from equilibrium relaxes toward a symmetric state faster than a system that starts closer to it. While this phenomenon is well-documented in various quantum systems, it remained unclear whether it could survive in the presence of strong Hilbert-space fragmentation (HSF). HSF occurs in systems with multiple conservation laws—such as simultaneous charge and dipole conservation—which partition the Hilbert space into exponentially many disconnected Krylov sectors.

The authors investigate this using three complementary frameworks: random quantum circuits, a pair-hopping Hamiltonian, and a dissipative pair-flip model. To handle the complexity of large systems, they develop a replica tensor-network (RTN) formulation for charge- and dipole-conserving gates, allowing them to compute the annealed Rnyi-2 entanglement asymmetry for systems up to 128 sites. They complement this with exact vector simulations using Chebyshev polynomial methods and an analytically solvable dissipative model to isolate the role of Krylov sectors in the relaxation process.

The study reveals a higher-order symmetric quantum Mpemba effect. In fragmented systems, the charge and dipole asymmetries exhibit Mpemba-like crossings on distinct timescales. The researchers identify a clear mechanism: the Hilbert space is divided into frozen sectors, which are dynamically inactive and retain a finite, non-decaying asymmetry, and active sectors, which host the relaxation processes. The Mpemba effect emerges from the dynamics within these active fragments, while the frozen fragments provide a persistent memory of the initial state. This framework shows that fragmentation does not destroy the Mpemba effect but rather reshapes it into a combination of frozen memory and active-fragment relaxation.