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

Abstract

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 transition 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 are consistent with those of a self-dual version of the model, namely correlation lengths exponents ${\nu }_x=2/3$ in the direction of the asymmetry and ${\nu }_y=1$ perpendicular to it, an incommensurability exponent $\bar{\beta }=2/3$, a specific heat exponent that keeps the value $\alpha =1/3$ 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 comment13 pages, 11 figures

References in corpus (19)

• Probing many-body dynamics on a 51-atom quantum simulator
• Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator
• Corner Transfer Matrix Renormalization Group Method
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Competing density-wave orders in a one-dimensional hard-boson model
• Mott insulators in strong electric fields
• Free parafermions
• Numerical study of the chiral ${\mathbb{Z}}_3$ quantum phase transition in one spatial dimension
• Quantum field theory for the chiral clock transition in one spatial dimension
• Phase diagram of the $Z_3$ Parafermionic Chain with Chiral Interactions
• Floating phase versus chiral transition in a 1D hard-boson model
• Liquid ground state, gap and excited states of a strongly correlated spin chain
• Critical phenomena at perfect and non-perfect surfaces
• Critical Exponents of the Chiral Potts Model from Conformal Field Theory
• Anisotropic scaling and generalized conformal invariance at Lifshitz points
• Dynamic Critical Behavior of the Swendsen-Wang Algorithm: The Two-Dimensional 3-State Potts Model Revisited
• Diagnosing Potts criticality and two-stage melting in one-dimensional hard-boson models
• The Many Faces of the Chiral Potts Model
• The Chiral Potts Models Revisited

Cited by in corpus (9)

• Lifshitz point at commensurate melting of 1D Rydberg atoms
• Conformal and chiral phase transitions in Rydberg chains
• Fidelity susceptibility as a diagnostic of the commensurate-incommensurate transition: A revisit of the programmable Rydberg chain
• Commensurate-incommensurate transition in the chiral Ashkin-Teller model
• Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm
• Dynamical phase transition and scaling in the chiral clock Potts chain
• Possible continuous transition from fractional quantum Hall to stripe phase at ${\nu }_e=7/3$
• Tensor network investigation of the hard-square model
• Emergent U(1) symmetry in non-particle-conserving one-dimensional models