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.

References in corpus (34)

• Quantum information with Rydberg atoms
• The physics of dipolar bosonic quantum gases
• Realizing a lattice spin model with polar molecules
• Bose-Einstein Condensation of Erbium
• Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas
• Quantum Phase Transitions and Vortex Dynamics in Superconducting Networks
• Quantum degenerate dipolar Fermi gas
• Long-range interacting quantum systems
• Classical critical behavior of spin models with long-range interactions
• Continuous Symmetry Breaking in a Two-dimensional Rydberg Array
• Continuous symmetry breaking and a new universality class in 1D long-range interacting quantum systems
• Anomalous Behavior of Spin Systems with Dipolar Interactions
• Criticality and Phase Diagram of Quantum Long-Range $\text{O(N)}$ models
• The boundary between long-range and short-range critical behavior
• Relations between Short Range and Long Range Ising models
• Berezinskii-Kosterlitz-Thouless transition in two-dimensional dipole systems
• Fixed Points Structure & Effective Fractional Dimension for O(N) Models with Long-Range Interactions
• Kosterlitz-Thouless behavior in layered superconductors: the role of the vortex-core energy
• Large-scale Monte Carlo simulation of two-dimensional classical XY model using multiple GPUs
• The crossover region between long-range and short-range interactions for the critical exponents
• Influence of long-range interactions on the critical behavior of the Ising model
• Field-linked resonances of polar molecules
• Upper and Lower Critical Decay Exponents of Ising Ferromagnets with Long-range Interaction
• Monte Carlo studies of the chiral and spin orderings of the three-dimensional Heisenberg spin glass
• Berezinskii-Kosterlitz-Thouless transition on regular and Villain types of $q$-state clock models
• Two-dimensional SIR epidemics with long range infection
• $BKT$ transitions in classical and quantum long-range systems
• Monte Carlo study of duality and the Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional $q$-state clock model in flow representations
• Clock Monte Carlo methods
• The low-temperature phase in the two-dimensional long-range diluted XY model
• Ion Trap Long-Range XY Model for Quantum State Transfer and Optimal Spatial Search
• Reentrance of Berezinskii-Kosterlitz-Thouless-like transitions in three-state Potts antiferromagnetic thin film
• Logarithmic finite-size scaling of the self-avoiding walk at four dimensions
• Villain model with long-range couplings

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