Two-dimensional XY Ferromagnet Induced by Long-range Interaction

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 $\sim 1/r^{2+\sigma }$. 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 $\sigma \le 2$, 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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Cited by in corpus (6)

• Clock Factorized Quantum Monte Carlo Method for Long-range Interacting Systems
• High-temperature partition functions and classical simulatability of long-range quantum systems
• Persistence of the Berezinskii-Kosterlitz-Thouless transition with long-range couplings
• One-dimensional long-range Ising model: two (almost) equivalent approximations
• Crossover in the Ordered Phase in the Non-Mermin-Wagner-Hohenberg Regime of Spin Models with Long-Range Coupling
• Long-Range Order in a Strictly Short-Range Quasi-2D XY Model: When Critical Fluctuations Matter