Helicity modulus in the bilayer XY model by worm algorithm
arXiv:2407.11507 · doi:10.1103/PhysRevB.111.094415
Abstract
The behaviour of the helicity modulus has been frequently employed to investigate the onset of the topological order characterizing the low-temperature phase of the two-dimensional XY-model. We here present how the analysis based on the use of this key quantity can be applied to the study of the properties of coupled layers. To this aim, we first discuss how to extend the popular worm algorithm to a layered sample, and in particular to the evaluation of the longitudinal helicity, that we introduce taking care of the fact that the virtual twist representing the elastic deformation one applies to properly define the helicity modulus can act on a single layer or on all of them. We then apply the method to investigate the bilayer XY-model, showing how the helicity modulus can be used to determine the phase diagram of the model as a function of temperature and inter-layer coupling strength
10 pages, 5 figures
References in corpus (38)
- Topological Phases in Two-Dimensional Materials: A Brief Review
- Worm Algorithm for Continuous-space Path Integral Monte Carlo Simulations
- Long-range interacting quantum systems
- A superfluid-droplet crystal and a free-space supersolid in a dipole-blockaded gas
- Quantum Monte Carlo study of S=1/2 weakly-anisotropic antiferromagnets on the square lattice
- Tensor renormalization group study of classical XY model on the square lattice
- Probability-Changing Cluster Algorithm for Two-Dimensional XY and Clock Models
- Large-scale Monte Carlo simulation of two-dimensional classical XY model using multiple GPUs
- Detection of XY behaviour in weakly anisotropic quantum antiferromagnets on the square lattice
- Quantum anomaly and 2D-3D crossover in strongly interacting Fermi gases
- Functional renormalization group approach to the sine-Gordon model
- Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition
- High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class
- Field-induced XY behavior in the S=1/2 antiferromagnet on the square lattice
- Direct Evidence of the Discontinuous Character of the Kosterlitz-Thouless Jump
- Experimental realization of field-induced XY and Ising ground states in a quasi-2D S=1/2 Heisenberg antiferromagnet
- transitions in classical and quantum long-range systems
- Phases of dipolar bosons in a bilayer geometry
- Nonperturbative renormalization group treatment of amplitude fluctuations for topological phase transitions
- Interplay of spin waves and vortices in the 2D XY model at small vortex-core energy
- Universal alternating order around impurities in antiferromagnets
- Supersolid phases of bosonic particles in a bubble trap
- Superfluid transition and specific heat of the 2D x-y model: Monte Carlo simulation
- Phase coherence of pairs of Cooper pairs as quasi-long-range order of half-vortex pairs in a two-dimensional bilayer system
- DMRG study of the Berezinskii-Kosterlitz-Thouless transitions of the 2D five-state clock model
- Sine-Gordon description of Beresinskii-Kosterlitz-Thouless physics at finite magnetic field
- Magnetism in the two-dimensional dipolar XY model
- Reentrant behavior of the phase stiffness in Josephson junction arrays
- Finite-temperature phases of trapped bosons in a two-dimensional quasiperiodic potential
- Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems
- Sine-Gordon Model - Renormalization Group Solutions and Applications
- BKT-paired phase in coupled XY models
- Electron-Hole Interference in an Inverted-Band Semiconductor Bilayer
- Self-consistent harmonic approximation with non-local couplings
- Monte Carlo simulations on rare-earth Holmium ultra-thin films
- Anisotropic Ginzburg-Landau and Lawrence-Doniach Models for Layered Ultracold Fermi Gases
- Villain model with long-range couplings
- Uniaxial modulation and the Berezinskii-Kosterlitz-Thouless transition