Entropic Barriers and the Kinetic Suppression of Topological Defects

TL;DR

Entropic barriers offer a passive route to stabilize quantum phases at finite temperature by coupling topological defects to mesoscopic reservoirs, producing a temperature-dependent free-energy barrier. The authors demonstrate the mechanism in an exactly solvable entropic Ising chain and in a two-dimensional entropic toric code, where defect suppression and hindered diffusion yield substantial stability improvements in finite systems, and they propose a concrete dual-species Rydberg experiment to realize the concept. They also extend the idea to the XY model, showing vortex-core-energy renormalization that enhances finite-size coherence and shifts the BKT crossover, illustrating broad applicability to both discrete and continuous topological orders. Overall, entropic protection provides a scalable, hardware-level strategy to extend coherence and memory lifetimes in realistic quantum devices, complementing active error correction and heralding new avenues for stabilizing quantum matter in the NISQ era.

Abstract

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.

Figures (3)

• Figure 1: Correlation length as a function of thermal energy $1/\beta$. Parameters are chosen as $M=50$, $\epsilon=10^{-3}$, $J=50$.
• Figure 2: (a) Schematic of the proposed dual-species Rydberg atom array, which consists of target spins (blue, $^{87}$Rb), sensor atoms (red, $^{133}$Cs), and bath atoms (yellow, $^{133}$Cs). Each sensor serves as a messenger between the system lattice and a local entropic reservoir formed by the bath cluster. (b) Conditional blockade via Rydberg dressing. The relevant energy levels $|g\rangle, |e\rangle,$ and $|r\rangle$ correspond to the ground, excited, and Rydberg states of the Cs atoms. An off-resonant laser with Rabi frequency $\Omega$ and negative detuning $|\Delta| \gg \Omega$ dresses the excited state, creating $|e'\rangle$ with a small admixture of Rydberg $|r\rangle$. This induces strong van der Waals interactions $\propto J_i$ between the sensor and surrounding bath atom $i$. The resulting total energy shift, $\sum J_i$, enforces the energetic penalty for defects. Crucially, the entropic stabilization relies on the degenerate bath configurations rather than precise energy matching, making the protocol robust against variations in interaction strengths $J_i$ arising from different inter-atomic distances $R_i$ between the bath and sensor atoms.
• Figure 3: Correlation length as a function of thermal energy for different values of $J'$.