Emergent Intermediate Phase in the $J_1$-$J_2$ XY model from Tensor Network Approaches

Abstract

We investigate the finite-temperature phase diagram of the classical $J_1$-$J_2$ XY model on a square lattice using a tensor network approach designed for frustrated spin systems. This model, characterized by competing nearest-neighbor and next-to-nearest-neighbor interactions, exhibits a complex interplay between $U(1)$ and $Z_2$ symmetries. Our study reveals an emergent intermediate phase around $J_2/J_1\sim 0.505$, which is characterized by a $Z_2$ long-range stripe order without phase coherence in the XY spins. The intermediate phase features two well-separated phase transitions: a higher-temperature Ising transition and a lower-temperature Berezinskii-Kosterlitz-Thouless transition. The relative separation between these transitions is significantly larger than previously reported, enabling a clearer investigation of their distinct thermodynamic properties. For $0.5<J_2/J_1<0.501$, two transitions merge into a single first-order phase transition, a phenomenon that cannot be explained solely by mapping to the Ising-XY model. As $J_2/J_1\to \infty$, the transition evolves continuously into the BKT universality class. These findings advance the understanding of the mechanisms driving phase transitions in frustrated spin systems and suggest potential experimental realizations in platforms such as ultracold atoms, Josephson junction arrays, and optical lattices.

12 pages, 9 figures

References in corpus (31)

• Entanglement Entropy and Quantum Field Theory
• Quantum simulation of frustrated magnetism in triangular optical lattices
• Engineering Ising-XY spin models in a triangular lattice via tunable artificial gauge fields
• Variational optimization algorithms for uniform matrix product states
• Tangent-space methods for uniform matrix product states
• Observation of Bose-Einstein Condensation in a Strong Synthetic Magnetic Field
• Ashkin-Teller criticality and pseudo first-order behavior in a frustrated Ising model on the square lattice
• Diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods
• Multicritical behavior in the fully frustrated XY model and related systems
• Universality away from critical points in two-dimensional phase transitions
• Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the Bose-Hubbard and XXZ models
• A scaling hypothesis for matrix product states
• Phase-transitions induced by easy-plane anisotropy in the classical Heisenberg antiferromagnet on a triangular lattice: a Monte Carlo simulation
• Monte Carlo study of the Villain version of the fully frustrated XY model
• A Monte Carlo analysis of the phase transitions in the 2D, $J_1-J_2$ XY model
• Spin and chiral orderings of the antiferromagnetic XY model on the triangular lattice and their critical properties
• Tensor network approach to the two-dimensional fully frustrated XY model and a chiral ordered phase
• Solving frustrated Ising models using tensor networks
• Spin-chirality decoupling and critical properties of a two-dimensional fully frustrated XY model
• Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell
• Phase diagram of the restricted solid-on-solid model coupled to the Ising model
• Cluster algorithms for frustrated two dimensional Ising antiferromagnets via dual worm constructions
• The fully frustrated XY model revisited: A new universality class
• Weak first-order phase transitions in the frustrated square lattice J1-J2 classical Ising model
• Tensor network approach to the fully frustrated XY model on a kagome lattice with a fractional vortex-antivortex pairing transition
• The 2D J_1-J_2 XY and XY-Ising Models
• Probing XY phase transitions in a Josephson junction array with tunable frustration
• Unified tensor network theory for frustrated classical spin models in two dimensions
• CFT description of the Fully Frustrated XY model and phase diagram analysis
• Observation of Chiral-Mode Domains in a Frustrated XY Model on Optical Triangular Lattices
• Emergent topological ordered phase for the Ising-XY Model revealed by cluster-updating Monte-Carlo method

Cited by in corpus (1)

• Two-dimensional $J_1$-$J_2$ clock model: Enhanced symmetries, emergent orders, and Landau-incompatible transitions