© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2609.29400

Thermal quasi-Devil's staircase in an anisotropic triangular-lattice Rydberg array

Jinghao Cao, Siyi Yang, Jingya Wang, Dong-Xu Liu, Zheng Yan

Published Sep 24, 2026• 0 citations

Abstract

A Devil's staircase is a sequence of transitions between topological sectors as a control parameter is varied. Such staircases are predicted in frustrated magnets and lattice gauge theories, but observing them is hard: the winding number that labels each sector is topologically protected, so local quantum dynamics alone cannot move the system from one step to the next. Here we propose and analyze an experimentally feasible way to realize a thermal quasi-Devil's staircase in a finite Rydberg-atom array. We study the anisotropic triangular-lattice Ising antiferromagnet using a dimer mapping, a directed-string description, exact thermodynamics, and Monte Carlo simulations. In the defect-free string manifold, the commensurate--incommensurate onset follows from a simple energy--entropy balance, and the exact Ising critical relation reduces to the same condition when triangle-rule defects are rare. On a finite lattice, this onset appears as a quasi-Devil's staircase of winding-sector crossovers, which we resolve through winding distributions, structure factors, and directional correlations. The key point is that thermal fluctuations overcome the topological barriers that block sector changes under purely quantum dynamics, and the staircase exists precisely at the finite sizes and tunable effective temperatures of current Rydberg platforms. This makes the effect directly observable in existing experiments. Our comparison also shows that the finite-size steps are not phase transitions: in the thermodynamic limit only a single phase transition survives, and the system crosses over to a defect-dominated paramagnet.

DOI: 10.48550/arxiv.2609.29400

Related papers

Topological Devil’s Staircase in a Constrained Kagome Ising Antiferromagnet

Afonso Rufino, Samuel Nyckees, Jeanne Colbois +1 more

We show that the constrained Ising model on the kagome lattice with infinite first and third neighbor couplings undergoes an infinite series of thermal first-order transitions at which, as in the Kasteleyn transition, linear defects of infinite length condense. However, their density undergoes abrupt jumps because of the peculiar structure of the low temperature phase, which is only partially ordered and hosts a finite density of zero-energy domain walls. The number of linear defects between consecutive zero-energy domain walls is quantized to integer values, leading to a devil's staircase of topological origin. By contrast to the devil's staircase of the anisotropic next-nearest neighbor Ising and related models, the wave vector is not fixed to commensurate values inside each phase.

arXiv:2505.05889•Physical Review Letters•Jan 14, 2026•1 citation

Quantum Catalysis of Magnetic Phase Transitions in a Quantum Simulator

Philip Richerme, Crystal Senko, S. É. Korenblit +5 more

We control quantum fluctuations to create the ground state magnetic phases of a classical Ising model with a tunable longitudinal magnetic field using a system of 6 to 10 atomic ion spins. Because of the long-range Ising interactions, the various ground state spin configurations are separated by multiple first-order phase transitions, which in our zero temperature system cannot be driven by thermal fluctuations. We instead use a transverse magnetic field as a quantum catalyst to observe the first steps of the complete fractal devil's staircase, which emerges in the thermodynamic limit and can be mapped to a large number of many-body and energy-optimization problems.

arXiv:1303.6983•Physical Review Letters•Sep 5, 2013•39 citations

Phase Transitions and Remnants of Fractionalization at Finite Temperature in the Triangular Lattice Quantum Loop Model

Xiaoxue Ran, Sylvain Capponi, Junchen Rong +2 more

The quantum loop and dimer models are archetypal correlated systems with local constraints. With natural foundations in statistical mechanics, they are of direct relevance to various important physical concepts and systems, such as topological order, lattice gauge theories, geometric frustrations, or more recently Rydberg array quantum simulators. However, how the thermal fluctuations interact with constraints has not been explored in the important class of nonbipartite geometries. Here we study, via unbiased quantum Monte Carlo simulations and field theoretical analysis, the finite-temperature phase diagram of the quantum loop model on the triangular lattice. We discover that the recently identified, "hidden" vison plaquette (VP) quantum crystal [X. Ran et al., Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice, Commun. Phys. 7, 207 (2024)CMPYEL0868-316610.1038/s42005-024-01680-z] experiences a finite-temperature continuous transition, which smoothly connects to the (2+1)d Cubic* quantum critical point separating the VP and Z_{2} quantum spin liquid phases. This finite-temperature phase transition acquires a unique property of "remnants of fractionalization" at finite temperature, in that, both the cubic order parameter-the plaquette loop resonance-and its constituent-the vison field-exhibit independent criticality signatures. This phase transition is connected to a three-state Potts transition between the lattice nematic phase and the high-temperature disordered phase. We discuss the relevance of our results for current experiments on quantum simulation platforms.

arXiv:2412.01503•Physical Review Letters•Aug 27, 2025•1 citation

Entropic Barriers and the Kinetic Suppression of Topological Defects

Yi-Lin Tsao, Zhu-Xi Luo

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.

quant-pharXiv:2602.16777•Feb 20, 2026•0 citations

Order by disorder and an emergent Kosterlitz-Thouless phase in a triangular Rydberg array

Sibo Guo, Juntao Huang, Jiangping Hu +1 more

A programmable quantum simulator using Rydberg-atom array provides a promising route to demystifying quantum many-body physics in strongly correlated systems. Motivated by the recent realization of various quantum magnetic phases on the frustrated Rydberg-atom array, we perform numerically exact quantum Monte Carlo simulations to investigate the exotic states of matter emerging in the model describing the Rydberg atom on a triangular lattice. Our state-of-the-art simulation unveils the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ triangular antiferromagnetic order exists at $1/3$ or $2/3$-Rydberg filling, consistent with the observation in experiments. Remarkably, $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ long-range order arising from order-by-disorder mechanism emerges at $1/2$ filling. At finite temperature, $\mathrm{U}(1)$ symmetry is emergent at $1/2$ filling and a Kosterlitz-Thouless phase transition occurs with increasing temperature. These intriguing phenomena are potentially detected in future Rydberg-atom experiments.

arXiv:2302.08963•Physical Review A•Nov 13, 2023•8 citations

Two-Stage Melting in Systems of Strongly Interacting Rydberg Atoms

Hendrik Weimer, Hans Peter Büchler

We analyze the ground state properties of a one-dimensional cold atomic system in a lattice, where Rydberg excitations are created by an external laser drive. In the classical limit, the ground state is characterized by a complete devil's staircase for the commensurate solid structures of Rydberg excitations. Using perturbation theory and a mapping onto an effective low-energy Hamiltonian, we find a transition of these commensurate solids into a floating solid with algebraic correlations. For stronger quantum fluctuations the floating solid eventually melts within a second quantum phase transition and the ground state becomes paramagnetic.

arXiv:1007.2189•Physical Review Letters•Nov 30, 2010•108 citations

A Devil's staircase is a sequence of transitions between topological sectors as a control parameter is varied. Such staircases are predicted in frustrated magnets and lattice gauge theories, but observing them is hard: the winding number that labels each sector is topologically protected, so local quantum dynamics alone cannot move the system from one step to the next. Here we propose and analyze an experimentally feasible way to realize a thermal quasi-Devil's staircase in a finite Rydberg-atom array. We study the anisotropic triangular-lattice Ising antiferromagnet using a dimer mapping, a directed-string description, exact thermodynamics, and Monte Carlo simulations. In the defect-free string manifold, the commensurate--incommensurate onset follows from a simple energy--entropy balance, and the exact Ising critical relation reduces to the same condition when triangle-rule defects are rare. On a finite lattice, this onset appears as a quasi-Devil's staircase of winding-sector crossovers, which we resolve through winding distributions, structure factors, and directional correlations. The key point is that thermal fluctuations overcome the topological barriers that block sector changes under purely quantum dynamics, and the staircase exists precisely at the finite sizes and tunable effective temperatures of current Rydberg platforms. This makes the effect directly observable in existing experiments. Our comparison also shows that the finite-size steps are not phase transitions: in the thermodynamic limit only a single phase transition survives, and the system crosses over to a defect-dominated paramagnet.

We show that the constrained Ising model on the kagome lattice with infinite first and third neighbor couplings undergoes an infinite series of thermal first-order transitions at which, as in the Kasteleyn transition, linear defects of infinite length condense. However, their density undergoes abrupt jumps because of the peculiar structure of the low temperature phase, which is only partially ordered and hosts a finite density of zero-energy domain walls. The number of linear defects between consecutive zero-energy domain walls is quantized to integer values, leading to a devil's staircase of topological origin. By contrast to the devil's staircase of the anisotropic next-nearest neighbor Ising and related models, the wave vector is not fixed to commensurate values inside each phase.

We control quantum fluctuations to create the ground state magnetic phases of a classical Ising model with a tunable longitudinal magnetic field using a system of 6 to 10 atomic ion spins. Because of the long-range Ising interactions, the various ground state spin configurations are separated by multiple first-order phase transitions, which in our zero temperature system cannot be driven by thermal fluctuations. We instead use a transverse magnetic field as a quantum catalyst to observe the first steps of the complete fractal devil's staircase, which emerges in the thermodynamic limit and can be mapped to a large number of many-body and energy-optimization problems.

The quantum loop and dimer models are archetypal correlated systems with local constraints. With natural foundations in statistical mechanics, they are of direct relevance to various important physical concepts and systems, such as topological order, lattice gauge theories, geometric frustrations, or more recently Rydberg array quantum simulators. However, how the thermal fluctuations interact with constraints has not been explored in the important class of nonbipartite geometries. Here we study, via unbiased quantum Monte Carlo simulations and field theoretical analysis, the finite-temperature phase diagram of the quantum loop model on the triangular lattice. We discover that the recently identified, "hidden" vison plaquette (VP) quantum crystal [X. Ran et al., Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice, Commun. Phys. 7, 207 (2024)CMPYEL0868-316610.1038/s42005-024-01680-z] experiences a finite-temperature continuous transition, which smoothly connects to the (2+1)d Cubic* quantum critical point separating the VP and Z_{2} quantum spin liquid phases. This finite-temperature phase transition acquires a unique property of "remnants of fractionalization" at finite temperature, in that, both the cubic order parameter-the plaquette loop resonance-and its constituent-the vison field-exhibit independent criticality signatures. This phase transition is connected to a three-state Potts transition between the lattice nematic phase and the high-temperature disordered phase. We discuss the relevance of our results for current experiments on quantum simulation platforms.

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.

A programmable quantum simulator using Rydberg-atom array provides a promising route to demystifying quantum many-body physics in strongly correlated systems. Motivated by the recent realization of various quantum magnetic phases on the frustrated Rydberg-atom array, we perform numerically exact quantum Monte Carlo simulations to investigate the exotic states of matter emerging in the model describing the Rydberg atom on a triangular lattice. Our state-of-the-art simulation unveils the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ triangular antiferromagnetic order exists at

1/3

or

2/3

-Rydberg filling, consistent with the observation in experiments. Remarkably, $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ long-range order arising from order-by-disorder mechanism emerges at

1/2

filling. At finite temperature,

\mathrm{U}(1)

symmetry is emergent at

1/2

filling and a Kosterlitz-Thouless phase transition occurs with increasing temperature. These intriguing phenomena are potentially detected in future Rydberg-atom experiments.

We analyze the ground state properties of a one-dimensional cold atomic system in a lattice, where Rydberg excitations are created by an external laser drive. In the classical limit, the ground state is characterized by a complete devil's staircase for the commensurate solid structures of Rydberg excitations. Using perturbation theory and a mapping onto an effective low-energy Hamiltonian, we find a transition of these commensurate solids into a floating solid with algebraic correlations. For stronger quantum fluctuations the floating solid eventually melts within a second quantum phase transition and the ground state becomes paramagnetic.