2017/11/14 by Francisco Hyunkyu Kim, Francisco H. Kim, Karlo Penc +2 · 2 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Antisymmetric relation #Boson #Irreducible representation #Ising model #Lattice (music) #Mathematical physics #Order (exchange) #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum mechanics #Square lattice #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.96.205142
published as Phys. Rev. B 96, 205142 (2017) · 13 pages, 4 figures
arxiv created 2017/11/14 · openalex publication_date 2017/11/22 · openalex created_date 2017/12/04 · arxiv updated 2019/02/12 · openalex updated_date 2026/08/05
The extension of the linear flavor-wave theory to fully antisymmetric irreducible representations (irreps) of SU(N) is presented in order to investigate the color order of SU(N) antiferromagnetic Heisenberg models in several two-dimensional geometries. The square, triangular, and honeycomb lattices are considered with m fermionic particles per site. We present two different methods: the first method is the generalization of the multiboson spin-wave approach to SU(N) which consists of associating a Schwinger boson to each state on a site. The second method adopts the Read and Sachdev bosons which are an extension of the Schwinger bosons that introduces one boson for each color and each line of the Young tableau. The two methods yield the same dispersing modes, a good indication that they properly capture the semiclassical fluctuations, but the first one leads to spurious flat modes of finite frequency not present in the second one. Both methods lead to the same physical conclusions otherwise: long-range N'eel-type order is likely for the square lattice for SU(4) with two particles per site, but quantum fluctuations probably destroy order for more than two particles per site, with N=2m. By contrast, quantum fluctuations always lead to corrections larger than the classical order parameter for the tripartite triangular lattice (with N=3m) or the bipartite honeycomb lattice (with N=2m) for more than one particle per site, m>1, making the presence of color very unlikely except maybe for m=2 on the honeycomb lattice, for which the correction is only marginally larger than the classical order parameter.