When long-range interactions switch off the quantum Mpemba effect

A counterintuitive race back to equilibrium

The name “Mpemba effect” comes from the observation that, in some circumstances, hotter water can freeze faster than cooler water. Its quantum counterpart is not simply about temperature: it describes cases where a system that begins farther from equilibrium can relax faster than another, initially closer state.

Hallam and colleagues examine one proposed route to this effect: the restoration of a symmetry that the initial state breaks. Picture many tiny spins, each pointing in a chosen direction. If the rules governing their evolution respect a symmetry—such as rotations around a chosen axis—the system may gradually lose the initial state’s preference for one direction. The researchers use a measure called entanglement asymmetry to track how much that symmetry is broken in a small part of the system. If the measure for two starting states crosses, the initially more asymmetric state has caught up in this particular sense: a signature of the quantum Mpemba effect in the study’s definition.

The key question is how that crossing changes when spins interact over different distances, and when the initial state carries different energy.

A model and numerical approach

The paper studies a one-dimensional spin-1/2 XYZ chain, with spin interactions that fall off as a power of the distance between spins and with a magnetic field applied along the chain’s z-axis. The power-law exponent controls the interaction range: larger exponents mean interactions diminish more quickly with distance, while smaller ones mean more long-range coupling.

The researchers numerically simulate the chain after preparing it in selected spin configurations and allowing it to evolve. They use time-dependent variational simulations with infinite matrix-product states, a computational method that represents an effectively infinite chain without tracking every spin independently. They also compare different initial-state families and energy densities, and estimate where the model’s equilibrium state develops broken symmetry.

A strong field creates an important intermediate regime called prethermalization. The system behaves for an extended period as though it has an effective continuous U(1) symmetry, even though the original XYZ interactions do not generally have that exact symmetry. The reported Mpemba behavior is therefore a prediction for this prethermal window, not a claim that the system remains in that regime forever.

What the simulations indicate

In the simulated cases, the effect appears when the field is strong enough to establish the emergent symmetry and the interactions are sufficiently short-ranged. Under those conditions, the symmetry can be restored during the dynamics, and the asymmetry curves for different starting states cross.

With sufficiently long-range interactions, the effective model can instead support a symmetry-broken state. The system then retains a nonzero symmetry-breaking signal rather than restoring the symmetry in the same way, and the crossing can disappear. In this sense, changing the interaction range offers a theoretical way to tune or halt the effect. The authors connect this pattern to the Hohenberg–Mermin–Wagner theorem, which constrains spontaneous breaking of continuous symmetries in low-dimensional systems with short-range interactions; sufficiently long-range interactions can evade that constraint.

The boundary is not set by interaction range alone. It shifts with the initial state’s energy density: higher-energy states generally require longer-range interactions to stabilize symmetry breaking and stop the observed crossing. The authors also find that the dynamical threshold and the estimated ground-state symmetry-breaking boundary do not coincide. A ground state can be ordered while the finite-energy states reached in a quench still show symmetry restoration and a finite Mpemba time.

What remains uncertain

These are numerical results for a specified model and a chosen diagnostic, not a direct experimental demonstration of this particular tunable scenario. The principal simulations use an infinite-chain approximation; real devices have finite numbers of spins. The paper’s supplementary analysis notes that finite-size effects become harder to control as interactions become longer-ranged, and that a finite observation window can complicate deciding whether a crossing has truly stopped or is merely delayed. Estimates of the symmetry-breaking boundary also carry uncertainty, and the phase diagram depends on the starting states and subsystem used to measure asymmetry.

The authors report checks using an alternative distance-based diagnostic and other initial states, which support aspects of the conclusions, but do not eliminate those limits. They suggest trapped ions, polar molecules and nitrogen-vacancy centers as platforms where tunable interactions could make the predictions testable. That is a proposed experimental direction, not evidence that the effect has already been observed in these systems.

The source is an arXiv preprint: a research manuscript made publicly available, not by itself proof of peer review or independent confirmation. Its central contribution is a model-based result: interaction range, field strength and initial-state energy can jointly shape whether symmetry restoration produces a quantum Mpemba crossing.