Interplay of spin waves and vortices in the 2D XY model at small vortex-core energy

Abstract

The Berezinskii-Kosterlitz-Thouless (BKT) mechanism describes universal vortex unbinding in many two-dimensional systems, including the paradigmatic XY model. However, most of these systems present a complex interplay between excitations at different length scales that complicates theoretical calculations of nonuniversal thermodynamic quantities. These difficulties may be overcome by suitably modifying the initial conditions of the BKT flow equations to account for noncritical fluctuations at small length scales. In this work, we perform a systematic study of the validity and limits of this two-step approach by constructing optimised initial conditions for the BKT flow. We find that the two-step approach can accurately reproduce the results of Monte-Carlo simulations of the traditional XY model. In order to systematically study the interplay between vortices and spin-wave excitations, we introduce a modified XY model with increased vortex fugacity. We present large-scale Monte-Carlo simulations of the spin stiffness and vortex density for this modified XY model and show that even at large vortex fugacity, vortex unbinding is accurately described by the nonperturbative functional renormalisation group.

References in corpus (16)

• Exact evolution equation for the effective potential
• Localization of preformed Cooper-pairs in disordered superconductors
• Phase fluctuations in a strongly disordered s-wave superconductor close to the metal-insulator transition
• Observation of the Berezinskii-Kosterlitz-Thouless Phase Transition in an Ultracold Fermi Gas
• Quantum critical behaviour in the superfluid density of strongly underdoped ultrathin cuprate films
• Kosterlitz-Thouless behavior in layered superconductors: the role of the vortex-core energy
• From local to critical fluctuations in lattice models: a non-perturbative renormalization-group approach
• Large-scale Monte Carlo simulation of two-dimensional classical XY model using multiple GPUs
• Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition
• Universal thermodynamics of a two-dimensional Bose gas
• Evidence of Two-Dimensional Quantum Critical Behavior in the Superfluid Density of Deeply Underdoped Bi2Sr2CaCu2O8+x
• Nonperturbative renormalization group treatment of amplitude fluctuations for $|\phi {|}^4$ topological phase transitions
• Coupled superfluidity of binary Bose mixtures in two dimensions
• Dual lattice functional renormalization group for the Berezinskii-Kosterlitz-Thouless transition: irrelevance of amplitude and out-of-plane fluctuations
• Correlated Non-Gaussian phase fluctuations in LaAlO${}_3$/SrTiO${}_3$ heterointerface
• Coarse grained models of stripe forming systems: phase diagrams, anomalies and scaling hypothesis

Cited by in corpus (14)

• Observation of the BKT Transition in a 2D Bose Gas via Matter-Wave Interferometry
• Shell-shaped atomic gases
• Unified tensor network theory for frustrated classical spin models in two dimensions
• Self-consistent harmonic approximation with non-local couplings
• Melting of the two-dimensional solid phase in the Gaussian-core model
• Berezinskii-Kosterlitz-Thouless phase transition with Rabi-coupled bosons
• Monte Carlo study of the phase transitions in the classical XY ferromagnets with random anisotropy
• Nonlinear diode effect and Berezinskii-Kosterlitz-Thouless transition in purely two-dimensional noncentrosymmetric superconductors
• Vortex supersolid in the XY model with tunable vortex fugacity
• Helicity modulus in the bilayer XY model by worm algorithm
• Ordering kinetics and steady states of XY-model with ferromagnetic and nematic interaction
• CNN-Based Vortex Detection in Atomic 2D Bose Gases in the Presence of a Phononic Background
• Uniformly frustrated XY model: strengthening of the vortex lattice by intrinsic disorder
• Berezinskii-Kosterlitz-Thouless phase transitions with long-range couplings