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arXiv · 2404.08498

Two-dimensional XY Ferromagnet Induced by Long-range Interaction

Tianning Xiao·Dingyun Yao·Chao Zhang·Zhijie Fan·Youjin Deng
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Abstract

The crossover between short-range and long-range (LR) universal behaviors remains a central theme in the physics of long-range interacting systems. The competition between LR coupling and the Berezinskii-Kosterlitz-Thouless mechanism makes the problem more subtle and less understood in the two-dimensional (2D) XY model, a cornerstone for investigating low-dimensional phenomena and their implications in quantum computation. We study the 2D XY model with algebraically decaying interaction $\sim1/r^{2+\sigma}$. Utilizing an advanced update strategy, we conduct large-scale Monte Carlo simulations of the model up to a linear size of $L=8192$. Our results demonstrate continuous phase transitions into a ferromagnetic phase for $\sigma \leq 2$, which exhibits the simultaneous emergence of a long-ranged order and a power-law decaying correlation function due to the Goldstone mode. Furthermore, we find logarithmic scaling behaviors in the low-temperature phase at $\sigma = 2$. The observed scaling behaviors in the low-temperature phase for $\sigma \le 2$ agree with our theoretical analysis. Our findings request further theoretical understandings and can be of practical application in cutting-edge experiments like Rydberg atom arrays.

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Tianning Xiao, Dingyun Yao, Chao Zhang, Zhijie Fan, Youjin Deng. 2024-04-12. Two-dimensional XY Ferromagnet Induced by Long-range Interaction. https://doi.org/10.1088/0256-307x%2F42%2F7%2F070002

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