### Abstract

We use the coupled cluster method (CCM) to study the zero-temperature ground-state (GS) properties of a spin-12 J1-J2 Heisenberg antiferromagnet on a triangular lattice with competing nearest-neighbor and next-nearest-neighbor exchange couplings J1>0 and J2≡κJ1>0, respectively, in the window 0≤κ<1. The classical version of the model has a single GS phase transition at κcl=18 in this window from a phase with 3-sublattice antiferromagnetic (AFM) 120 Néel order for κ<κcl to an infinitely degenerate family of 4-sublattice AFM Néel phases for κ>κcl. This classical accidental degeneracy is lifted by quantum fluctuations, which favor a 2-sublattice AFM striped phase. For the quantum model we work directly in the thermodynamic limit of an infinite number of spins, with no consequent need for any finite-size scaling analysis of our results. We perform high-order CCM calculations within a well-controlled hierarchy of approximations, which we show how to extrapolate to the exact limit. In this way we find results for the case κ=0 of the spin-12 model for the GS energy per spin, E/N=-0.5521(2)J1, and the GS magnetic order parameter, M=0.198(5) (in units where the classical value is Mcl=12), which are among the best available. For the spin-12 J1-J2 model we find that the classical transition at κ=κcl is split into two quantum phase transitions at κ1c=0.060(10) and κ2c=0.165(5). The two quasiclassical AFM states (viz., the 120 Néel state and the striped state) are found to be the stable GS phases in the regime κ<κ1c and κ>κ2c, respectively, while in the intermediate regimes κ1c<κ<κ2c the stable GS phase has no evident long-range magnetic order.

Original language | English (US) |
---|---|

Article number | 014426 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 91 |

Issue number | 1 |

DOIs | |

State | Published - Jan 22 2015 |

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*Physical Review B - Condensed Matter and Materials Physics*,

*91*(1), [014426]. https://doi.org/10.1103/PhysRevB.91.014426

**Quasiclassical magnetic order and its loss in a spin- 12 Heisenberg antiferromagnet on a triangular lattice with competing bonds.** / Li, P. H.Y.; Bishop, R. F.; Campbell, Charles E.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 91, no. 1, 014426. https://doi.org/10.1103/PhysRevB.91.014426

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TY - JOUR

T1 - Quasiclassical magnetic order and its loss in a spin- 12 Heisenberg antiferromagnet on a triangular lattice with competing bonds

AU - Li, P. H.Y.

AU - Bishop, R. F.

AU - Campbell, Charles E

PY - 2015/1/22

Y1 - 2015/1/22

N2 - We use the coupled cluster method (CCM) to study the zero-temperature ground-state (GS) properties of a spin-12 J1-J2 Heisenberg antiferromagnet on a triangular lattice with competing nearest-neighbor and next-nearest-neighbor exchange couplings J1>0 and J2≡κJ1>0, respectively, in the window 0≤κ<1. The classical version of the model has a single GS phase transition at κcl=18 in this window from a phase with 3-sublattice antiferromagnetic (AFM) 120 Néel order for κ<κcl to an infinitely degenerate family of 4-sublattice AFM Néel phases for κ>κcl. This classical accidental degeneracy is lifted by quantum fluctuations, which favor a 2-sublattice AFM striped phase. For the quantum model we work directly in the thermodynamic limit of an infinite number of spins, with no consequent need for any finite-size scaling analysis of our results. We perform high-order CCM calculations within a well-controlled hierarchy of approximations, which we show how to extrapolate to the exact limit. In this way we find results for the case κ=0 of the spin-12 model for the GS energy per spin, E/N=-0.5521(2)J1, and the GS magnetic order parameter, M=0.198(5) (in units where the classical value is Mcl=12), which are among the best available. For the spin-12 J1-J2 model we find that the classical transition at κ=κcl is split into two quantum phase transitions at κ1c=0.060(10) and κ2c=0.165(5). The two quasiclassical AFM states (viz., the 120 Néel state and the striped state) are found to be the stable GS phases in the regime κ<κ1c and κ>κ2c, respectively, while in the intermediate regimes κ1c<κ<κ2c the stable GS phase has no evident long-range magnetic order.

AB - We use the coupled cluster method (CCM) to study the zero-temperature ground-state (GS) properties of a spin-12 J1-J2 Heisenberg antiferromagnet on a triangular lattice with competing nearest-neighbor and next-nearest-neighbor exchange couplings J1>0 and J2≡κJ1>0, respectively, in the window 0≤κ<1. The classical version of the model has a single GS phase transition at κcl=18 in this window from a phase with 3-sublattice antiferromagnetic (AFM) 120 Néel order for κ<κcl to an infinitely degenerate family of 4-sublattice AFM Néel phases for κ>κcl. This classical accidental degeneracy is lifted by quantum fluctuations, which favor a 2-sublattice AFM striped phase. For the quantum model we work directly in the thermodynamic limit of an infinite number of spins, with no consequent need for any finite-size scaling analysis of our results. We perform high-order CCM calculations within a well-controlled hierarchy of approximations, which we show how to extrapolate to the exact limit. In this way we find results for the case κ=0 of the spin-12 model for the GS energy per spin, E/N=-0.5521(2)J1, and the GS magnetic order parameter, M=0.198(5) (in units where the classical value is Mcl=12), which are among the best available. For the spin-12 J1-J2 model we find that the classical transition at κ=κcl is split into two quantum phase transitions at κ1c=0.060(10) and κ2c=0.165(5). The two quasiclassical AFM states (viz., the 120 Néel state and the striped state) are found to be the stable GS phases in the regime κ<κ1c and κ>κ2c, respectively, while in the intermediate regimes κ1c<κ<κ2c the stable GS phase has no evident long-range magnetic order.

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U2 - 10.1103/PhysRevB.91.014426

DO - 10.1103/PhysRevB.91.014426

M3 - Article

AN - SCOPUS:84921810678

VL - 91

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 1

M1 - 014426

ER -