Quantum field theory for the chiral clock transition in one spatial dimension

Abstract

We describe the quantum phase transition in the $N$-state chiral clock model in spatial dimension $d=1$. With couplings chosen to preserve time-reversal and spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-dimensional chain of trapped ultracold alkali atoms. For such couplings and $N=3$, the clock model is expected to have a direct phase transition from a gapped phase with a broken global ${\mathbb{Z}}_N$ symmetry, to a gapped phase with the ${\mathbb{Z}}_N$ symmetry restored. The transition has dynamical critical exponent $z\ne 1$, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in $d=1$, involving the onset of a single boson condensate in the background of a higher-dimensional $N$-boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in $2-d$, with $4-N$ chosen to be of order $2-d$. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for $N=3$, finding good evidence for a direct phase transition, and obtain estimates for $z$ and the correlation length exponent $\nu$.

arXiv comment51 pages, 15 figures; (v2) added 2 figures to introduction

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• Emergent ${\mathbb{Z}}_2$ gauge theories and topological excitations in Rydberg atom arrays
• Kibble-Zurek exponent and chiral transition of the period-4 phase of Rydberg chains
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• Emergent glassy behavior in a kagome Rydberg atom array
• Microscopic characterization of Ising conformal field theory in Rydberg chains
• Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics
• Lifshitz point at commensurate melting of 1D Rydberg atoms
• Diagnosing Potts criticality and two-stage melting in one-dimensional hard-boson models
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• Fidelity susceptibility as a diagnostic of the commensurate-incommensurate transition: A revisit of the programmable Rydberg chain
• Unconventional U(1) to ${\mathbf{Z}}_{\mathbf{q}}$ cross-over in quantum and classical $\mathbf{q}$-state clock models
• Trimer quantum spin liquid in a honeycomb array of Rydberg atoms
• Emergent conformal boundaries from finite-entanglement scaling in matrix product states
• Truncation effects in the charge representation of the O(2) model
• Anomalous suppression of large-scale density fluctuations in classical and quantum spin liquids
• Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning
• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Commensurate-incommensurate transition in the chiral Ashkin-Teller model
• Spontaneous symmetry breaking without ground state degeneracy in generalized $N$-state clock model
• Dynamical phase transition and scaling in the chiral clock Potts chain
• Tunable quantum criticality in multicomponent Rydberg arrays
• Resolving chiral transitions in Rydberg arrays with quantum Kibble-Zurek mechanism and finite-time scaling
• Identifying the Huse-Fisher universality class of the three-state chiral Potts model
• Eight-vertex criticality in the interacting Kitaev chain
• ${\mathbb{Z}}_N$ lattice gauge theory in a ladder geometry
• Nonequilibrium critical dynamics in the quantum chiral clock model
• Realizing and Probing Baryonic Excitations in Rydberg Atom Arrays
• Non-invertible duality and symmetry topological order of one-dimensional lattice models with spatially modulated symmetry
• Open Quantum Rotors: Connecting Correlations and Physical Currents
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• Critical properties of the quantum Ashkin-Teller chain with chiral perturbations
• Pivoting through the chiral-clock family
• Discrete Abelian lattice gauge theories on a ladder and their dualities with quantum clock models
• Lattice Defects in Rydberg Atom Arrays
• Possible continuous transition from fractional quantum Hall to stripe phase at ${\nu }_e=7/3$
• Floating Phases in One-Dimensional Rydberg Ising Chains
• Exploring quantum criticality and ergodicity-breaking dynamics in spin-1 Kitaev chains via single-ion anisotropies
• Thermalization at Low Temperatures via Weakly-Damped Multi-Site Baths
• Tensor network investigation of the hard-square model
• Quantum clock models with infinite-range interactions
• Geometric phase and multipartite entanglement of Rydberg atom chains
• Temperature dependence of energy transport in the ${\mathbb{Z}}_3$ chiral clock model
• ${\mathbb{Z}}_4$ transitions in quantum loop models on a zig-zag ladder
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• Engineering a Josephson junction chain for the simulation of the clock model
• Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array
• Chiral and Clock phases in Twisted Dipolar Clusters
• Energy transport in Z3 chiral clock model
• Doped resonating-valence-bond states: Robustness of the spin-ice phases in three-dimensional Rydberg arrays
• Phase diagram of an extended parafermion chain
• Emergent U(1) symmetry in non-particle-conserving one-dimensional models
• Qubit encodings for lattices of dipolar planar rotors