2017/09/30 by Han Ma · 2 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Boson #Combinatorics #Condensed matter physics #Duality (order theory) #Geometry #Homogeneous space #Ising model #Lattice (music) #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Valence bond theory #Vortex #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.97.045104
published in Physical review. B./Physical review. B 97(4) (American Physical Society) · Published version
openalex publication_date 2018/01/05 · arxiv created 2018/01/09 · arxiv updated 2018/01/17 · openalex created_date 2019/08/13 · openalex updated_date 2026/08/06
Motivated by recent numerical work, we use the boson-vortex duality to study the possible phases of the frustrated spin-(1)/(2)\phantom\rule4pt0exJ1\text\ensuremath-J2 XXZ models on the honeycomb lattice. By condensing the vortices, we obtain various gapped phases that either break certain lattice symmetry or preserve all the symmetries. The gapped phases breaking lattice symmetries occur when the vortex band structure has two minima. Condensing one of the two vortex flavors leads to an Ising ordered phase, while condensing both vortex flavors gives rise to a valence-bond-solid state. Both of those phases have been observed in the numerical studies of the J1\text\ensuremath-J2 XXZ honeycomb model. Furthermore, by tuning the band structure of vortex and condensing it at the \mathrm\ensuremathΓ point, we obtain a featureless paramagnet. But the precise nature of this featureless state is still unclear and needs future study.