### 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.

Original language | English |
---|---|

Article number | 205142 |

Journal | Physical Review B |

Volume | 96 |

Issue number | 20 |

DOIs | |

Publication status | Published - Nov 22 2017 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B*,

*96*(20), [205142]. https://doi.org/10.1103/PhysRevB.96.205142

**Linear flavor-wave theory for fully antisymmetric SU(N) irreducible representations.** / Kim, Francisco H.; Penc, K.; Nataf, Pierre; Mila, Frédéric.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 96, no. 20, 205142. https://doi.org/10.1103/PhysRevB.96.205142

}

TY - JOUR

T1 - Linear flavor-wave theory for fully antisymmetric SU(N) irreducible representations

AU - Kim, Francisco H.

AU - Penc, K.

AU - Nataf, Pierre

AU - Mila, Frédéric

PY - 2017/11/22

Y1 - 2017/11/22

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85039940665&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevB.96.205142

DO - 10.1103/PhysRevB.96.205142

M3 - Article

AN - SCOPUS:85039940665

VL - 96

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 20

M1 - 205142

ER -