Berezinskii-Kosterlitz-Thouless transitions in classical and quantum long-range systems
Year: 2022
Authors: Giachetti G., Trombettoni A., Ruffo S., Defenu N.
Autors Affiliation: Scuola Int Super Avanzati SISSA, Via Bonomea 265, I-34136 Trieste, Italy; Ist Nazl Fis Nucl, Sez Trieste, Via Bonomea 265, I-34136 Trieste, Italy; Univ Trieste, Dept Phys, Str Costiera 11, I-34151 Trieste, Italy; CNR, Ist Sistemi Complessi, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy; Swiss Fed Inst Technol, Inst Theoret Phys, Wolfgang Pauli Str 27, Zurich, Switzerland.
Abstract: In the past decades, considerable efforts have been made to understand the critical features of both classical and quantum long-range (LR) interacting models. The case of the Berezinskii-Kosterlitz-Thouless (BKT) universality class, as in the two-dimensional (2D) classical XY model, is considerably complicated by the presence, for short-range interactions, of a line of renormalization group fixed points. In this paper, we discuss a field-theoretical treatment of the 2D XY model with LR couplings, and we compare it with results from the self-consistent harmonic approximation. These methods lead to a rich phase diagram, where both power law BKT scaling and spontaneous symmetry breaking appear for the same (intermediate) decay rates of LR interactions. We also discuss the Villain approximation for the 2D XY model with power law couplings, providing hints that, in the LR regime, it fails to reproduce the correct critical behavior. The obtained results are then applied to the LR quantum XXZ spin chain at zero temperature. We discuss the relation between the phase diagrams of the two models, and we give predictions about the scaling of the order parameter of the quantum chain close to the transition.
Journal/Review: PHYSICAL REVIEW B
Volume: 106 (1) Pages from: 14106-1 to: 14106-15
More Information: This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster). This work is part of the MIUR-PRIN2017 project Coarse-grained description for non-equilibrium systems and transport phenomena (CO-NEST) No. 201798CZL. The authors acknowledge the MISTI Global Seed Funds MIT-FVG collaboration grants NV centers for the test of the Quantum Jarzynski Equality (NVQJE) and Non-Equilibrium Thermodynamics of Dissipative Quantum Systems.KeyWords: Phase-transitions; Field-theory; Coulomb Gas; Ferromagnets; Plane; Renormalization; Magnetization; Dynamics; Duality; ModelsDOI: 10.1103/PhysRevB.106.014106Citations: 10data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-10-20References taken from IsiWeb of Knowledge: (subscribers only)