Chern-Simons fermionization approach to two-dimensional quantum magnets: Implications for antiferromagnetic magnons and unconventional quantum phase transitions

2017/09/30 by Rui Wang, Baigeng Wang, Tigran Sedrakyan +1
Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Condensed matter physics #Electron #Fermion #Ferromagnetism #Frustration #Gauge theory #Magnon #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum mechanics #Quantum phase transition #Quantum spin liquid #Spin polarization #Topological Materials and Phenomena #Topological quantum computer #cond-mat.str-el #cond-mat.supr-con

paper · pdf · doi:10.1103/physrevb.98.064402

published as Phys. Rev. B 98, 064402 (2018) · 15 pages, 4 figures, revtex4

openalex created_date 2017/09/15 · arxiv created 2018/03/23 · openalex publication_date 2018/08/02 · arxiv updated 2018/08/08 · openalex updated_date 2026/08/05

Abstract

We develop an approach to describe antiferromagnetic magnons on a bipartite lattice supporting the N'eel state using fractionalized degrees of freedom typically inherent to quantum spin liquids. In particular, we consider a long-range magnetically ordered state of interacting two-dimensional quantum spin-1/2 XY models using the Chern-Simons (CS) fermion representation of interacting spins. The interaction leads to Cooper instability and pairing of CS fermions, and to CS superconductivity which spontaneously violates the continuous U(1) symmetry generating a linearly dispersing gapless Nambu-Goldstone mode due to phase fluctuations. We evaluate this mode and show that it is in high-precision agreement with magnons of the corresponding N'eel antiferromagnet irrespective to the lattice symmetry. Using the fermion formulation of the system with frustration, we show that the competing interactions emerge in the form of long-range interaction vertices mediated by the CS gauge field, which are responsible for restoring the continuous symmetry at sufficiently strong frustration. We identify these new interaction vertices and discuss their implications for unconventional phase transitions. We also apply the proposed theory to a model of anyons that can be tuned continuously from fermions to bosons, and discuss the results.

Citations

• Bold Diagrammatic Monte Carlo Technique: When the Sign Problem Is Welcome
• Periodic table for topological insulators and superconductors
• Classification of topological quantum matter with symmetries
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Classification of topological insulators and superconductors in three spatial dimensions
• Continuous transition between fractional quantum Hall and superfluid states
• Holographic matter: Deconfined string at criticality
• Equivalence of the resonating-valence-bond and fractional quantum Hall states
• Magnons and excitation continuum in XXZ triangular antiferromagnetic model: Application toBa3CoSb2O9
• Large-Nexpansion for frustrated quantum antiferromagnets
• Fractional quantum Hall effect and Chern-Simons gauge theories
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Deconfined Criticality Flow in the Heisenberg Model with Ring-Exchange Interactions
• Polaron Problem by Diagrammatic Quantum Monte Carlo
• Chiral spin states and superconductivity
• Unpaired Majorana fermions in quantum wires
• Quantum Spin Liquids
• Quantum orders and symmetric spin liquids