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 extendedO(2) model by adding a γ cos (q φ ) term to the ordinary O(2) model with angular values restricted to a 2 π interval. In the γ →∞ 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 π 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 spacetime dimensions using Monte Carlo and tensor renormalization group methods. Both the specific heat and the magnetic susceptibility show a doublepeak structure for fractional q . In case 1, the smallβ peak is associated with a crossover, and the largeβ 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 Δ q and the system is close to the smallβ BerezinskiiKosterlitzThouless transition, the system has a magnetic susceptibility that scales as ∼1 /(Δ q )1^{1 /δ'} with δ^{'} estimates consistent with the magnetic critical exponent δ =15 . The crossover peak and the Ising critical point move to BerezinskiiKosterlitzThouless transition points with the same powerlaw scaling. A phase diagram for this model in the (β ,q ) plane is sketched. These results are possibly relevant for configurable Rydbergatom arrays where the interpolations among phases with discrete symmetries can be achieved by varying continuously the distances among atoms and the detuning frequency.
 Publication:

Physical Review D
 Pub Date:
 September 2021
 DOI:
 10.1103/PhysRevD.104.054505
 arXiv:
 arXiv:2105.10450
 Bibcode:
 2021PhRvD.104e4505H
 Keywords:

 High Energy Physics  Lattice;
 Condensed Matter  Statistical Mechanics;
 Physics  Computational Physics
 EPrint:
 23 pages, 38 figures, 2 tables