Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2203.01163 · Physical Review Research

Conformal and chiral phase transitions in Rydberg chains

Ivo A. Maceira, Natalia Chepiga, Frédéric Mila

Published Nov 14, 2022• 29 citations
arXivHTMLPDF

Abstract

Using density matrix renormalization group simulations on open chains, we map out the wave vector in the incommensurate disordered phase of a realistic model of Rydberg chains with $1/{r}^{6}$ interactions, and we locate and characterize the points along the commensurate lines where the transition out of the period 3 and 4 phases is conformal. We confirm that it is three-state Potts for the period-3 phase, and we show that it is Ashkin-Teller with $\ensuremath{\nu}\ensuremath{\simeq}0.80$ for the period-4 phase. We further show that close to these points, the transition is still continuous, but with a completely different scaling of the wave vector, in agreement with a chiral transition. Finally, we propose to use the conformal points as benchmarks for Kibble-Zurek experiments, defining a roadmap towards a conclusive identification of the chiral universality class.

DOI
10.1103/physrevresearch.4.043102

Related papers

Kibble-Zurek exponent and chiral transition of the period-4 phase of Rydberg chains

Natalia Chepiga, Frédéric Mila

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.

arXiv:2001.06698•Nature Communications•Jan 18, 2021•49 citations

Identifying the Huse-Fisher universality class of the three-state chiral Potts model

Samuel Nyckees, Jeanne Colbois, Frédéric Mila

Using the corner-transfer matrix renormalization group approach, we revisit the three-state chiral Potts model on the square lattice, a model proposed in the eighties to describe commensurate-incommensurate transitions at surfaces, and with direct relevance to recent experiments on chains of Rydberg atoms. This model was suggested by Huse and Fisher to have a chiral transition in the vicinity of the Potts point, a possibility that turned out to be very difficult to definitely establish or refute numerically. Our results confirm that the transition changes character at a Lifshitz point that separates a line of Pokrosky-Talapov transitions far enough from the Potts point from a line of direct continuous order-disorder transition close to it. Thanks to the accuracy of the numerical results, we have been able to base the analysis entirely on effective exponents to deal with the crossovers that have hampered previous numerical investigations. The emerging picture is that of a new universality class with exponents that do not change between the Potts point and the Lifshitz point, and that appear to be consistent with those of a self-dual version of the model, namely correlation lengths exponents νx=2/3 in the direction of the asymmetry and νy=1 perpendicular to it, an incommensurability exponent β¯=2/3, a specific heat exponent that keeps the value α=1/3 of the three-state Potts model, and a dynamical exponent z=3/2. These results are in excellent agreement with experimental results obtained on reconstructed surfaces in the nineties, and shed light on recent Kibble-Zurek experiments on the period-3 phase of chains of Rydberg atoms.

arXiv:2008.08408•Nuclear Physics B•Mar 5, 2021•9 citations

Commensurate-incommensurate transition in the chiral Ashkin-Teller model

Samuel Nyckees, Frédéric Mila

We investigate the classical chiral Ashkin-Teller model on a square lattice with the corner transfer matrix renormalization group algorithm. We show that the melting of the period-4 phase in the presence of a chiral perturbation takes different forms depending on the coefficient of the four-spin term in the Ashkin-Teller model. Close to the clock limit of two decoupled Ising models, the system undergoes a two-step commensurate-incommensurate transition as soon as the chirality is introduced, with an intermediate critical floating phase bounded by a Kosterlitz-Thouless transition at high temperature and a Pokrovsky-Talapov transition at low temperature. By contrast, close to the four-states Potts model, we argue for the existence of a unique commensurate-incommensurate transition that belongs to the chiral universality class, and for the presence of a Lifshitz point where the ordered, disordered, and floating phases meet. Finally, we map the whole phase diagram, which turns out to be in qualitative agreement with the 40-year-old prediction by Huse and Fisher.

arXiv:2109.01415•Physical Review Research•Feb 4, 2022•13 citations

Resolving chiral transitions in one-dimensional Rydberg arrays with quantum Kibble-Zurek mechanism and finite-time scaling

Jose Soto Garcia, Natalia Chepiga

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.

arXiv:2403.03081•Physical review. B./Physical review. B•Sep 9, 2024•12 citations

Critical properties of the quantum Ashkin-Teller chain with chiral perturbations

Bernhard E. Lüscher, Frédéric Mila, Natalia Chepiga

We investigate the nature of the phase transitions in the quantum Ashkin-Teller chain in the presence of chiral perturbations. We locate the Lifshitz line separating a region of direct chiral transitions from the region where the transition is through an intermediate floating phase. Furthermore, we identify a small region in the vicinity of the four-state Potts point where chiral perturbations are irrelevant and where the transition remains conformal. Implications to Rydberg atom experiments are briefly discussed.

arXiv:2308.07144•Physical review. B./Physical review. B•Nov 27, 2023•8 citations

Fidelity susceptibility as a diagnostic of the commensurate-incommensurate transition: A revisit of the programmable Rydberg chain

Xue-Jia Yu, Sheng Yang, Jing‐Bo Xu +1 more

In recent years, programmable Rydberg-atom arrays have been widely used to simulate new quantum phases and phase transitions, generating great interest among theorists and experimentalists. Based on the large-scale density matrix renormalization group method, the ground-state phase diagram of one-dimensional Rydberg chains is investigated with fidelity susceptibility as an efficient diagnostic method. We find that the competition between Rydberg blockade and external detuning produces unconventional phases and phase transitions. As the Rydberg blockade radius increases, the phase transition between disordered and density-wave ordered phases changes from the standard Potts universality class to an unconventional chiral one. As the radius increases further (above Potts point but still close to the tip of the lobe), a very narrow intermediate floating-phase region begins to appear. A concise physical picture is also provided to illustrate the numerical results. Compared with previous studies, this work brings more evidence for commensurate-incommensurate quantum phase transitions in programmable quantum simulators from the perspective of quantum information, showing that fidelity susceptibility can be used to study such phase transitions.

arXiv:2207.08337•Physical review. B./Physical review. B•Oct 24, 2022•26 citations
Using density matrix renormalization group simulations on open chains, we map out the wave vector in the incommensurate disordered phase of a realistic model of Rydberg chains with 1/r61/{r}^{6}1/r6 interactions, and we locate and characterize the points along the commensurate lines where the transition out of the period 3 and 4 phases is conformal. We confirm that it is three-state Potts for the period-3 phase, and we show that it is Ashkin-Teller with \ensuremathν\ensuremath≃0.80\ensuremath{\nu}\ensuremath{\simeq}0.80\ensuremathν\ensuremath≃0.80 for the period-4 phase. We further show that close to these points, the transition is still continuous, but with a completely different scaling of the wave vector, in agreement with a chiral transition. Finally, we propose to use the conformal points as benchmarks for Kibble-Zurek experiments, defining a roadmap towards a conclusive identification of the chiral universality class.
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.
Using the corner-transfer matrix renormalization group approach, we revisit the three-state chiral Potts model on the square lattice, a model proposed in the eighties to describe commensurate-incommensurate transitions at surfaces, and with direct relevance to recent experiments on chains of Rydberg atoms. This model was suggested by Huse and Fisher to have a chiral transition in the vicinity of the Potts point, a possibility that turned out to be very difficult to definitely establish or refute numerically. Our results confirm that the transition changes character at a Lifshitz point that separates a line of Pokrosky-Talapov transitions far enough from the Potts point from a line of direct continuous order-disorder transition close to it. Thanks to the accuracy of the numerical results, we have been able to base the analysis entirely on effective exponents to deal with the crossovers that have hampered previous numerical investigations. The emerging picture is that of a new universality class with exponents that do not change between the Potts point and the Lifshitz point, and that appear to be consistent with those of a self-dual version of the model, namely correlation lengths exponents νx=2/3 in the direction of the asymmetry and νy=1 perpendicular to it, an incommensurability exponent β¯=2/3, a specific heat exponent that keeps the value α=1/3 of the three-state Potts model, and a dynamical exponent z=3/2. These results are in excellent agreement with experimental results obtained on reconstructed surfaces in the nineties, and shed light on recent Kibble-Zurek experiments on the period-3 phase of chains of Rydberg atoms.
We investigate the classical chiral Ashkin-Teller model on a square lattice with the corner transfer matrix renormalization group algorithm. We show that the melting of the period-4 phase in the presence of a chiral perturbation takes different forms depending on the coefficient of the four-spin term in the Ashkin-Teller model. Close to the clock limit of two decoupled Ising models, the system undergoes a two-step commensurate-incommensurate transition as soon as the chirality is introduced, with an intermediate critical floating phase bounded by a Kosterlitz-Thouless transition at high temperature and a Pokrovsky-Talapov transition at low temperature. By contrast, close to the four-states Potts model, we argue for the existence of a unique commensurate-incommensurate transition that belongs to the chiral universality class, and for the presence of a Lifshitz point where the ordered, disordered, and floating phases meet. Finally, we map the whole phase diagram, which turns out to be in qualitative agreement with the 40-year-old prediction by Huse and Fisher.
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.
We investigate the nature of the phase transitions in the quantum Ashkin-Teller chain in the presence of chiral perturbations. We locate the Lifshitz line separating a region of direct chiral transitions from the region where the transition is through an intermediate floating phase. Furthermore, we identify a small region in the vicinity of the four-state Potts point where chiral perturbations are irrelevant and where the transition remains conformal. Implications to Rydberg atom experiments are briefly discussed.
In recent years, programmable Rydberg-atom arrays have been widely used to simulate new quantum phases and phase transitions, generating great interest among theorists and experimentalists. Based on the large-scale density matrix renormalization group method, the ground-state phase diagram of one-dimensional Rydberg chains is investigated with fidelity susceptibility as an efficient diagnostic method. We find that the competition between Rydberg blockade and external detuning produces unconventional phases and phase transitions. As the Rydberg blockade radius increases, the phase transition between disordered and density-wave ordered phases changes from the standard Potts universality class to an unconventional chiral one. As the radius increases further (above Potts point but still close to the tip of the lobe), a very narrow intermediate floating-phase region begins to appear. A concise physical picture is also provided to illustrate the numerical results. Compared with previous studies, this work brings more evidence for commensurate-incommensurate quantum phase transitions in programmable quantum simulators from the perspective of quantum information, showing that fidelity susceptibility can be used to study such phase transitions.