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.
Highlights
More than 40 years after its observation in thin 4He films [1], the Berezinskii-Kosterlitz-Thouless (BKT) transition [2,3,4,5] has registered in recent years an increasing interest in the field of low-dimensional strongly correlated electron systems
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 renormalization group
The procedure to connect the low-energy Coulomb gas description with the microscopic model by effective bare initial conditions in the BKT flow has been widely tested on the square-lattice
Summary
More than 40 years after its observation in thin 4He films [1], the Berezinskii-Kosterlitz-Thouless (BKT) transition [2,3,4,5] has registered in recent years an increasing interest in the field of low-dimensional strongly correlated electron systems. Our aim is to accurately test the two-step procedure by comparing the numerical results from Monte Carlo (MC) simulations with the RG two-step procedure for increasing values of the vortex fugacity To this end, we first extract the stiffness and vortex-core energy from low-temperature MC data and use them as initial conditions for the subsequent RG flow. We first extract the stiffness and vortex-core energy from low-temperature MC data and use them as initial conditions for the subsequent RG flow This procedure turns out to be rather successful for the standard XY model, with an excellent estimate of TBKT, despite some small discrepancy in the temperature evolution of the superfluid stiffness near the transition.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
