SISSA/ENS Researchers Find Quantum Mpemba Effect in Ising Models

Researchers at SISSA and ENS Paris-Saclay have introduced a new quantum-information measure, the Kramers-Wannier entanglement asymmetry, and found it exhibits a striking crossover between the ordered and disordered phases, together with a pronounced dip at the critical point in the transverse-field Ising chain. This dip becomes increasingly sharp as the subsystem size grows. Their work, focused on the behavior of the Kramers-Wannier duality away from criticality and out of equilibrium, reveals a quantum Mpemba effect where states initially farther from equilibrium can restore symmetry faster than those closer to it. This suggests that a system’s distance from balance can accelerate its return to symmetry, opening new perspectives on the dynamics of dualities in quantum many-body systems.

A newly defined quantum property exhibits a striking and measurable dip precisely at the critical point of a common model system. Their work centers on the transverse-field Ising chain and introduces the Kramers-Wannier entanglement asymmetry, a quantum-information measure designed to quantify the breaking of this specific symmetry. The team’s analysis of ground states away from criticality reveals a crossover between ferromagnetic and paramagnetic phases, alongside the aforementioned dip at the critical point. Importantly, this dip becomes increasingly sharp with increasing subsystem size, suggesting a heightened sensitivity to system dimensions as the material approaches a phase transition. This refined measurement capability is enabled by the Kramers-Wannier entanglement asymmetry, which provides a quantitative way to assess symmetry breaking. Researchers demonstrated that the Kramers-Wannier entanglement asymmetry decays to zero, signaling the dynamical restoration of the non-invertible symmetry. “Our results provide a first systematic characterization of the nonequilibrium dynamics of a non-invertible symmetry in lattice models,” establishing entanglement asymmetry as a powerful tool for probing these complex systems and opening new avenues for understanding duality dynamics.

The exploration of quantum symmetries has expanded beyond traditional, invertible forms to encompass non-invertible symmetries like Kramers-Wannier duality. Understanding their behavior outside of idealized critical points and in dynamic, real-world scenarios remained largely uncharted territory until recently.

Researchers are increasingly focused on understanding how quantum symmetries behave in dynamic, real-world conditions, moving beyond idealized equilibrium scenarios. Milo Vescovo at SISSA and ENS Paris-Saclay, alongside Pasquale Calabrese and Filiberto Ares, have been investigating the Kramers-Wannier duality, a fundamental concept in quantum physics, specifically examining its properties when a system is not at a stable equilibrium. This Kramers-Wannier entanglement asymmetry allows researchers to quantify how much a quantum state deviates from possessing this particular symmetry. Initial investigations into equilibrium states reveal a striking crossover between the ferromagnetic and paramagnetic phases, punctuated by a significant feature at the critical point separating these phases. This sensitivity is crucial for understanding how the symmetry breaks down and reforms. Beyond observing static states, the researchers examined what happens when the system is abruptly changed, demonstrating that even when starting from vastly different initial conditions, the Kramers-Wannier symmetry is ultimately restored, as evidenced by the decay of the entanglement asymmetry to zero.

The subtle fingerprints of quantum symmetry can now be traced with unprecedented precision, potentially aiding the development of more robust quantum technologies. Researchers at SISSA and ENS Paris-Saclay have demonstrated a new method for characterizing a specific type of symmetry, the Kramers-Wannier duality, not just at stable equilibrium, but also during dynamic shifts in a quantum system. This work, focused on the transverse-field Ising chain, reveals how this duality behaves when pushed away from its usual, well-understood critical point and allowed to evolve freely. Central to this advance is the Kramers-Wannier entanglement asymmetry. Beyond static states, the investigation extended to how the symmetry responds to abrupt changes, with analytical and numerical evidence supporting this effect and pinpointing the underlying mechanism driving the accelerated restoration.

Researchers at SISSA in Italy and ENS Paris-Saclay in France authored this work while investigating the behavior of Kramers-Wannier duality, a non-invertible symmetry present in the transverse-field Ising chain. They demonstrated that the Kramers-Wannier entanglement asymmetry consistently decayed to zero over time, signaling the restoration of the non-invertible symmetry following these quenches, but the rate of restoration proved surprising.

The exploration of non-invertible symmetries in quantum systems has intensified, with the Kramers-Wannier duality serving as a central, yet incompletely understood, example. Traditionally studied at critical points defining phase transitions, recent work shifts focus to the duality’s behavior away from criticality and, crucially, out of equilibrium, a relatively uncharted territory. Researchers are leveraging a quantum-information measure, the Kramers-Wannier entanglement asymmetry, to probe these dynamic regimes.

This methodology centers on the transverse-field Ising chain, a model frequently used to study phase transitions, but with a focus on behavior away from the traditionally studied critical points. They demonstrated that even when starting from vastly different initial conditions, the Kramers-Wannier symmetry is ultimately restored, as evidenced by the decay of the entanglement asymmetry to zero.