Broken Quantum Symmetry Restores Itself Faster with Greater Initial Disruption

Sreemayee Aditya and colleagues at the Institute for Theoretical Physics have discovered a counterintuitive phenomenon where a quantum system restores broken symmetry more rapidly with stronger initial symmetry breaking, known as the quantum Mpemba effect. This effect persists even when conservation laws fragment the system’s Hilbert space, resolving a long-standing question. Their investigation, combining replica tensor-network formulations with Hamiltonian simulations and a dissipative model, reveals a higher-order symmetric quantum Mpemba effect manifesting in charge and dipole asymmetries across differing timescales. Fragmentation does not eliminate the quantum Mpemba effect, but instead reshapes it through a mechanism of frozen memory and active-fragment relaxation, offering a key understanding of this behaviour in systems with higher-moment symmetries.

Calculating entanglement asymmetry via replica tensor-networks in fragmented quantum systems

Replica tensor-networks proved central to unlocking calculations on systems far exceeding the limits of traditional simulation. The technique addresses the challenge of strong Hilbert-space fragmentation, where a system’s possible states become disconnected like a shattered mirror, each shard representing an isolated piece. Instead of directly simulating the complex quantum behaviour of every possible state, the replica tensor-network formulation averages over many identical copies of the system, simplifying the calculations. This averaging allows access to the annealed Rényi-2 entanglement asymmetry, a measure of how entangled two parts of a quantum system are, for systems containing up to 128 components. Simulations performed on random quantum circuits and Hamiltonians conserving both charge and dipole moment, alongside a dissipative model to explore symmetry restoration.

Replica tensor-networks reveal persistent accelerated symmetry restoration in fragmented quantum

Entanglement measures now reach up to L=128 components, exceeding previous limits of 20, thanks to the implementation of replica tensor-networks. The technique averages over multiple system copies to simplify calculations, enabling the investigation of strong Hilbert-space fragmentation, a phenomenon hindering traditional simulations. A higher-order symmetric quantum Mpemba effect was uncovered, demonstrating that both charge and dipole asymmetries exhibit Mpemba-like crossings on parametrically distinct timescales.

Dissecting the system into ‘frozen’ and ‘active’ Krylov sectors revealed that asymmetry is retained in frozen fragments, impeding full restoration, while active fragments drive accelerated relaxation. Entanglement measurements extended to L=128 components using replica tensor-networks, a sharp increase from previous limitations of 20 components, allowing detailed analysis of this fragmentation. Both random circuits and Hamiltonians conserving charge and dipole moment revealed that asymmetries exhibit Mpemba-like crossings, but on different timescales, indicating a complex interaction between the conserved quantities. Further analysis showed that asymmetry remains trapped within ‘frozen’ sectors, hindering complete symmetry restoration, while ‘active’ sectors drive accelerated relaxation. However, these results currently focus on relatively small system sizes and idealised conditions; scaling these simulations to realistically complex systems and accounting for environmental noise remains a substantial challenge.

Quantum Mpemba effect survives fragmentation via differing asymmetry relaxation rates

Researchers are increasingly focused on understanding how quantum systems handle disruption and return to equilibrium, a vital step towards utilising their power for computation and materials science. This latest work highlights a surprising complexity, however; the quantum Mpemba effect, where systems seemingly speed up symmetry restoration with greater initial imbalance, persists even when conservation laws fragment the system, though the precise mechanism remains elusive. The work reveals a ‘higher-order’ effect, with charge and dipole asymmetries relaxing at different rates, a subtlety that challenges existing models focused on single conserved quantities.

The finding that fragmented conservation laws reshape, rather than eliminate, this quantum Mpemba effect is significant. A persistent, albeit reshaped, quantum Mpemba effect was found even when a quantum system is fragmented into isolated parts, due to ‘frozen’ memories and active fragment relaxation. Systems obeying both charge and dipole conservation do not simply suppress the quantum Mpemba effect, where disruption paradoxically speeds recovery, but reshape it via distinct mechanisms within isolated portions of the system. Analysing these ‘frozen’ and ‘active’ sectors revealed that asymmetry is retained in the former, impeding complete restoration, while the latter drive the observed acceleration; Krylov sectors are, in effect, disconnected areas within a quantum system’s possible states.

The research demonstrated that the quantum Mpemba effect, where greater initial imbalance leads to faster symmetry restoration, persists even in quantum systems fragmented by conservation laws. This is significant because it shows that fragmentation does not eliminate this unusual behaviour, but instead reshapes it through differing relaxation rates in isolated sectors of the system. Researchers found asymmetry remains trapped in ‘frozen’ sectors, hindering full restoration, while ‘active’ sectors drive accelerated relaxation. The study, conducted on systems conserving both charge and dipole properties up to a size of 128, provides a framework for understanding this effect in systems with multiple symmetries.