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Symmetry Breaking in an Extended O(2) Model
Preprint   Open access

Symmetry Breaking in an Extended O(2) Model

Leon Hostetler, Ryo Sakai, Jin Zhang, Alexei Bazavov and Yannick Meurice
ArXiv.org
Cornell University
12/29/2023
DOI: 10.48550/arxiv.2312.17739
url
https://doi.org/10.48550/arxiv.2312.17739View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

Motivated by attempts to quantum simulate lattice models with continuous Abelian symmetries using discrete approximations, we study an extended-O(2) model in two dimensions that differs from the ordinary O(2) model by the addition of an explicit symmetry breaking term $-h_q\cos(q\varphi)$. Its coupling $h_q$ allows to smoothly interpolate between the O(2) model ($h_q=0$) and a $q$-state clock model ($h_q\rightarrow\infty$). In the latter case, a $q$-state clock model can also be defined for non-integer values of $q$. Thus, such a limit can also be considered as an analytic continuation of an ordinary $q$-state clock model to noninteger $q$. In previous work, we established the phase diagram of the model in the infinite coupling limit ($h_q\rightarrow\infty$). We showed that for non-integer $q$, there is a second-order phase transition at low temperature and a crossover at high temperature. In this work, we establish the phase diagram at finite values of the coupling using Monte Carlo and tensor methods. We show that for non-integer $q$, the second-order phase transition at low temperature and crossover at high temperature persist to finite coupling. For integer $q=2,3,4$, we know there is a second-order phase transition at infinite coupling (i.e. the well-known clock models). At finite coupling, we find that the critical exponents for $q=3,4$ vary with the coupling, and for $q=4$ the transition may turn into a BKT transition at small coupling. We comment on the similarities and differences of the phase diagrams with those of quantum simulators of the Abelian-Higgs model based on ladder-shaped arrays of Rydberg atoms.
 Physics - Computational Physics Physics - High Energy Physics - Lattice Physics - Statistical Mechanics

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