Entropic Barriers and the Kinetic Suppression of Topological Defects

Many quantum phases, from topological orders to superfluids, are destabilized at finite temperature by the proliferation and motion of topological defects such as anyons or vortices. Conventional protection mechanisms rely on energetic gaps and fail once thermal fluctuations exceed the gap scale. Here we examine a complementary mechanism of entropic protection, in which defect nucleation is suppressed by coupling to mesoscopic auxiliary reservoirs of dimension $M$, generating an effective free-energy barrier that increases with temperature. In the Ising chain, this produces a characteristic three-regime evolution of the correlation length as a function of temperature - linear growth, entropy-controlled plateau, and eventual breakdown - indicating a general modification of defect behavior. Focusing on two spatial dimensions, where true finite-temperature topological order is forbidden in the thermodynamic limit, we show that entropic protection can nevertheless strongly enhance stabilization at finite system size, the regime directly relevant for quantum memory and experiments. Owing to the topological character of the defects, creation and transport are independently suppressed, yielding a double parametric reduction of logical errors in the entropic toric code and enhanced coherence when the framework is extended to Berezinskii-Kosterlitz-Thouless transitions. Entropic barriers thus provide a passive and scalable route to stabilizing quantum phases in experimentally relevant regimes. We propose an experimental setup for entropic toric code using dual species Rydberg arrays with dressing.

💡 Research Summary

The paper introduces a novel “entropic protection” mechanism that stabilizes quantum phases against thermal proliferation of topological defects such as domain walls, anyons, or vortices. Instead of relying on an energetic gap that is overwhelmed at high temperature, the authors couple each defect to a mesoscopic auxiliary reservoir of dimension M. When a stabilizer is satisfied (no defect) the reservoir can explore M states, providing a large entropy; when a defect is present the reservoir is forced into a unique state, dramatically reducing its entropy. This asymmetry creates a free‑energy barrier that grows with temperature, suppressing both defect nucleation and motion.

The authors first illustrate the idea with an exactly solvable 1‑D Ising chain. By integrating out the reservoir they obtain Boltzmann weights w₊ and w₋ for satisfied and violated bonds, respectively. The correlation length ξ =