Clock model interpolation and symmetry breaking in O(2) models

Abstract

Motivated by recent attempts to quantum simulate lattice models with continuous Abelian symmetries using discrete approximations, we define an extended-O(2) model by adding a $\gamma \cos (q\phi )$ term to the ordinary O(2) model with angular values restricted to a $2\pi$ interval. In the $\gamma \to \infty$ limit, the model becomes an extended $q$-state clock model that reduces to the ordinary $q$-state clock model when $q$ is an integer and otherwise is a continuation of the clock model for noninteger $q$. By shifting the $2\pi$ integration interval, the number of angles selected can change discontinuously and two cases need to be considered. What we call case $1$ has one more angle than what we call case $2$. We investigate this class of clock models in two space-time dimensions using Monte Carlo and tensor renormalization group methods. Both the specific heat and the magnetic susceptibility show a double-peak structure for fractional $q$. In case $1$, the small-$\beta$ peak is associated with a crossover, and the large-$\beta$ peak is associated with an Ising critical point, while both peaks are crossovers in case $2$. When $q$ is close to an integer by an amount $\Delta q$ and the system is close to the small-$\beta$ Berezinskii-Kosterlitz-Thouless transition, the system has a magnetic susceptibility that scales as $\sim 1/(\Delta q{)}^{1-1/{\delta }^{\prime }}$ with ${\delta }^{\prime }$ estimates consistent with the magnetic critical exponent $\delta =15$. The crossover peak and the Ising critical point move to Berezinskii-Kosterlitz-Thouless transition points with the same power-law scaling. A phase diagram for this model in the $(\beta ,q)$ plane is sketched. These results are possibly relevant for configurable Rydberg-atom arrays where the interpolations among phases with discrete symmetries can be achieved by varying continuously the distances among atoms and the detuning frequency.

arXiv comment23 pages, 38 figures, 2 tables

References in corpus (52)

• Probing many-body dynamics on a 51-atom quantum simulator
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Tensor renormalization group approach to 2D classical lattice models
• Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator
• Simulating Lattice Gauge Theories within Quantum Technologies
• Quantum-Classical Computation of Schwinger Model Dynamics using Quantum Computers
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
• Coarse-graining renormalization by higher-order singular value decomposition
• Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
• Quantum Link Models: A Discrete Approach to Gauge Theories
• A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis
• QCD as a Quantum Link Model
• Towards analog quantum simulations of lattice gauge theories with trapped ions
• Dualities and the phase diagram of the $p$-clock model
• Tensor Networks for Lattice Gauge Theories with continuous groups
• A resource efficient approach for quantum and classical simulations of gauge theories in particle physics
• Simulation of Nonequilibrium Dynamics on a Quantum Computer
• Digital quantum simulation of lattice gauge theories in three spatial dimensions
• Exact blocking formulas for spin and gauge models
• Tensor renormalization group study of classical XY model on the square lattice
• Quantum simulation of the universal features of the Polyakov loop
• Probability-Changing Cluster Algorithm for Two-Dimensional XY and Clock Models
• Universality away from critical points in two-dimensional phase transitions
• Critical properties of the two-dimensional $q$-state clock model
• Large-scale Monte Carlo simulation of two-dimensional classical XY model using multiple GPUs
• Digitizing Gauge Fields: Lattice Monte Carlo Results for Future Quantum Computers
• Phase transition of four-dimensional Ising model with higher-order tensor renormalization group
• A qubit regularization of the $O(3)$ sigma model
• Response to a twist on systems with Zp symmetry
• A quantitative study of the Kosterlitz-Thouless phase transition in a system of two-dimensional plane rotators ( XY model ) by high temperature expansions through ${\beta }^{20}$
• Phase transition of the q-state clock model: duality and tensor renormalization
• Simulating the All-Order Strong Coupling Expansion III: O(N) sigma/loop models
• Berezinskii-Kosterlitz-Thouless transition on regular and Villain types of $q$-state clock models
• Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks
• Non-Kosterlitz-Thouless transitions for the $q$-state clock models
• Numerical study of the phase transitions in the two-dimensional Z(5) vector model
• Remarks on nuclear matter: how an ${\omega }_0$ condensate can spike the speed of sound, and a model of $Z(3)$ baryons
• Calculation of higher-order moments by higher-order tensor renormalization group
• Scaling and universality in the aging kinetics of the two-dimensional clock model
• True and quasi long-range order in the generalized $q$-state clock model
• Phase transitions in the ${\mathbb{Z}}_p$ and U(1) clock models
• High-temperature expansion of the magnetic susceptibility and higher moments of the correlation function for the two-dimensional XY model
• Finite-$m$ scaling analysis of Berezinskii-Kosterlitz-Thouless phase transitions and entanglement spectrum for the six-state clock model
• The two-dimensional O(3) model at nonzero density: from dual lattice simulations to repulsive bosons
• Truncation effects in the charge representation of the O(2) model
• The phase transitions in 2D Z(N) vector models for N>4
• Critical analysis of two-dimensional classical XY model
• Ordering kinetics in q-state clock model: scaling properties and growth laws
• Examples of symmetry-preserving truncations in tensor field theory
• Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories
• Phase transitions of the five-state clock model on the square lattice
• Cross derivative: a universal and efficient method for phase transitions in classical spin models

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