Linear flavor-wave theory for fully antisymmetric SU(N) irreducible representations

Francisco H. Kim, Karlo Penc, Pierre Nataf, and Frédéric Mila
Phys. Rev. B 96, 205142 – Published 22 November 2017

Abstract

The extension of the linear flavor-wave theory to fully antisymmetric irreducible representations (irreps) of SUN is presented in order to investigate the color order of SUN 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 SUN 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 Néel-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.

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  • Received 28 August 2017

DOI:https://doi.org/10.1103/PhysRevB.96.205142

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Francisco H. Kim1, Karlo Penc2,3, Pierre Nataf1, and Frédéric Mila1

  • 1Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
  • 2Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, H-1525 Budapest, P.O.B. 49, Hungary
  • 3MTA-BME Lendület Magneto-optical Spectroscopy Research Group, 1111 Budapest, Hungary

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Issue

Vol. 96, Iss. 20 — 15 November 2017

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