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arXiv:2505.12979 · Nature Communications

Tricritical Kibble-Zurek scaling in Rydberg atom ladders

Hanteng Wang, Xingyu Li, Chengshu Li

Published Nov 26, 2025• 12 citations

Abstract

The Kibble–Zurek (KZ) mechanism has been extensively studied in various second-order phase transitions, yet the case of tricriticality—the point where second-order phase transition lines terminate—remains experimentally elusive. Here, we theoretically propose probing KZ scaling at tricritical points using Rydberg atom arrays arranged as two- and three-leg ladders, which realize the tricritical Ising and tricritical Potts universality classes. By slowly ramping the Rabi frequency and detuning, we extract two relevant tricritical exponents, ν and ν', both via conventional paths from the disordered to the ordered phase and via “tangential” paths confined entirely within the disordered phase. At faster speeds, ramping dynamics go beyond the standard KZ paradigm: data collapse analysis using the parent critical exponents (rather than the tricritical ones) reveals renormalization group flows toward the adjacent second-order critical line, and we identify it as a dynamical analog of Zamolodchikov’s c-theorem. Our protocol is readily implementable on existing Rydberg quantum simulators. This provides a direct route to measuring distinct tricritical exponents which can reveal an emergent spacetime supersymmetry constraint 1/ν − 1/ν' = 1. Moreover, this work deepens our theoretical understanding and opens new avenues for exploring beyond-KZ quantum dynamics with rich renormalization group structure. The Kibble-Zurek mechanism describes universal dynamics near criticality. Here, the authors extend it to tricriticality using Rydberg atom ladders, proposing ramping protocols that measure two tricritical exponents and reveal emergent supersymmetry and dynamical renormalization group flow.

DOI: 10.1038/s41467-025-65652-9

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The Kibble–Zurek (KZ) mechanism has been extensively studied in various second-order phase transitions, yet the case of tricriticality—the point where second-order phase transition lines terminate—remains experimentally elusive. Here, we theoretically propose probing KZ scaling at tricritical points using Rydberg atom arrays arranged as two- and three-leg ladders, which realize the tricritical Ising and tricritical Potts universality classes. By slowly ramping the Rabi frequency and detuning, we extract two relevant tricritical exponents, ν and ν', both via conventional paths from the disordered to the ordered phase and via “tangential” paths confined entirely within the disordered phase. At faster speeds, ramping dynamics go beyond the standard KZ paradigm: data collapse analysis using the parent critical exponents (rather than the tricritical ones) reveals renormalization group flows toward the adjacent second-order critical line, and we identify it as a dynamical analog of Zamolodchikov’s c-theorem. Our protocol is readily implementable on existing Rydberg quantum simulators. This provides a direct route to measuring distinct tricritical exponents which can reveal an emergent spacetime supersymmetry constraint 1/ν − 1/ν' = 1. Moreover, this work deepens our theoretical understanding and opens new avenues for exploring beyond-KZ quantum dynamics with rich renormalization group structure. The Kibble-Zurek mechanism describes universal dynamics near criticality. Here, the authors extend it to tricriticality using Rydberg atom ladders, proposing ramping protocols that measure two tricritical exponents and reveal emergent supersymmetry and dynamical renormalization group flow.

Abstract The conventional Kibble–Zurek mechanism, describing driven dynamics across critical points based on the adiabatic-impulse scenario (AIS), has attracted broad attention. However, the driven dynamics at the tricritical point with two independent relevant directions have not been adequately studied. Here, we employ the time-dependent variational principle to study the driven critical dynamics at a one-dimensional supersymmetric Ising tricritical point. For the relevant direction along the Ising critical line, the AIS apparently breaks down. Nevertheless, we find that the critical dynamics can still be described by finite-time scaling in which the driving rate has a dimension of r μ = z + 1/ ν μ with z and ν μ being the dynamic exponent and correlation length exponent in this direction, respectively. For driven dynamics along another direction, the driving rate has a dimension of r p = z + 1/ ν p with ν p being another correlation length exponent. Our work brings a new fundamental perspective into nonequilibrium critical dynamics near the tricritical point, which could be realized in programmable quantum processors in Rydberg atomic systems.

The Kibble-Zurek scaling reveals the universal dynamics when a system is linearly ramped across a symmetry-breaking phase transition. However, in reality, inevitable finite-size effects or symmetry-breaking perturbations can often smear out the critical point and render the phase transition into a smooth crossover. In this Letter, we show experimentally that the precise Kibble-Zurek scaling can be retained in the near-critical crossover regime, not necessarily crossing the critical point strictly. The key ingredient to achieving this near-critical Kibble-Zurek scaling is that the system size and the symmetry-breaking field must be appropriately scaled following the variation of ramping speeds. The experiment is performed in a reconfigurable Rydberg atom array platform, where the Rydberg blockade effect induces a Z_{2} symmetry-breaking transition. The atom array platform enables precise control of the system size and the zigzag geometry as a symmetry-breaking field. Therefore, we can demonstrate notable differences in the precision of the Kibble-Zurek scaling with or without properly scaling the system size and the zigzag geometry. Our results strengthen the Kibble-Zurek scaling as an increasingly valuable tool for investigating phase transition in quantum simulation platforms.

Chains of Rydberg atoms have emerged as an amazing playground to study quantum physics in 1D. Playing with inter-atomic distances and laser detuning, one can in particular explore the commensurate-incommensurate transition out of density waves through the Kibble-Zurek mechanism, and the possible presence of a chiral transition with dynamical exponent z > 1. Here, we address this problem theoretically with effective blockade models where the short-distance repulsions are replaced by a constraint of no double occupancy. For the period-4 phase, we show that there is an Ashkin-Teller transition point with exponent ν = 0.78 surrounded by a direct chiral transition with a dynamical exponent z = 1.11 and a Kibble-Zurek exponent μ = 0.41. For Rydberg atoms with a van der Waals potential, we suggest that the experimental value μ = 0.25 is due to a chiral transition with z ≃ 1.9 and ν ≃ 0.47 surrounding an Ashkin-Teller transition close to the 4-state Potts universality.

The experimental realization of the quantum Kibble-Zurek mechanism in arrays of trapped Rydberg atoms has brought the problem of commensurate-incommensurate transition back into the focus of active research. Relying on equilibrium simulations of finite intervals, direct chiral transitions at the boundary of the period-3 and period-4 phases have been predicted. Here, we study how these chiral transitions can be diagnosed experimentally with critical dynamics. We demonstrate that chiral transitions can be distinguished from the floating phases by comparing Kibble-Zurek dynamics on arrays with different numbers of atoms. Furthermore, by sweeping in the opposite direction and keeping track of the order parameter, we identify the location of conformal points. Finally, combining forward and backward sweeps, we extract all critical exponents characterizing the transition.

Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics are governed by the universal properties associated with the QPT. The resulting quantum criticality has been explored by probing linear response for systems near thermal equilibrium. While time dependent phenomena associated with classical phase transitions have been studied in various scientific fields, understanding critical real-time dynamics in isolated, non-equilibrium quantum systems is of fundamental importance both for exploring novel approaches to quantum information processing and realizing exotic new phases of matter. Here, we use a Rydberg atom quantum simulator with programmable interactions to study the quantum critical dynamics associated with several distinct QPTs. By studying the growth of spatial correlations while crossing the QPT at variable speeds, we experimentally verify the quantum Kibble-Zurek mechanism (QKZM) for an Ising-type QPT, explore scaling universality, and observe corrections beyond simple QKZM predictions. This approach is subsequently used to investigate novel QPTs associated with chiral clock model providing new insights into exotic systems, and opening the door for precision studies of critical phenomena and applications to quantum optimization.

When a system is swept through a quantum critical point, the Kibble-Zurek mechanism predicts that the average number of topological defects follows a universal power-law scaling with the ramp timescale. This scaling behavior is determined by the equilibrium critical exponents of the underlying phase transition. We show that the correspondence between Kibble-Zurek scaling and quantum criticality does not hold generally. In particular, the defect density can exhibit a suppression faster than the Kibble-Zurek prediction even when the quench crosses a critical point, while conventional Kibble-Zurek scaling may persist for quenches through a noncritical point. Our results, based on models representative of a broad class of quasi-one-dimensional Fermi systems, identify the dynamical conditions under which universal defect scaling emerges and clarify the relation between defect generation and equilibrium criticality. © 2026 authors. Published by the American Physical Society.