Interplay of spin waves and vortices in the two-dimensional XY model at small vortex-core energy
Year: 2020
Authors: Maccari I., Defenu N., Benfatto L., Castellani C., Enss T.
Autors Affiliation: Royal Inst Technol, Dept Theoret Phys, SE-10691 Stockholm, Sweden; Heidelberg Univ, Inst Theoret Phys, D-69120 Heidelberg, Germany; Swiss Fed Inst Technol, Inst Theoret Phys, Wolfgang Pauli Str 27, CH-8093 Zurich, Switzerland; Sapienza Univ Rome, Dept Phys, Ple A Moro 2, I-00185 Rome, Italy; Inst Complex Syst ISC CNR, UOS Sapienza, Ple A Moro 5, I-00185 Rome, Italy.
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. 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 renormalization group.
Journal/Review: PHYSICAL REVIEW B
Volume: 102 (10) Pages from: 104505-1 to: 104505-12
More Information: We thank J. Lorenzana, N. Dupuis, G. Gori, and A. Trombettoni for stimulating discussions. This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via Project-ID 273811115 SFB1225 (ISOQUANT) and under Germanys Excellence Strategy EXC-2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster), by the Italian MAECI under the Italian-India collaborative project SUPERTOP-PGR04879, by the Italian MIUR Project PRIN 2017 No. 2017Z8TS5B, by Regione Lazio (L. R. 13/08) under Project SIMAP and by Sapienza University under project Ateneo 2019 (Grant No. RM11916B56802AFE).KeyWords: Renormalization-group; Phase-transitions; Critical-behavior; Monte-carlo; Superfluid Density; Coulomb Gas; Temperature; EquationDOI: 10.1103/PhysRevB.102.104505Citations: 13data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-10-20References taken from IsiWeb of Knowledge: (subscribers only)