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Bulletin of the American Physical Society

A Schwinger boson mean field study of the $J_1$-$J_2$ Heisenberg triangular-lattice quantum antiferromagnet

Dag-Vidar Bauer, John Ove Fjærestad

Published Mar 14, 2017• 0 citations
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A Schwinger boson mean field study of the J1J_1J1​-J2J_2J2​ Heisenberg triangular-lattice quantum antiferromagnet
We present the zero-temperature phase diagram of a Heisenberg antiferromagnet on a frustrated triangular lattice with nearest-neighbor (J1)({J}_{1})(J1​) and next-nearest-neighbor (J2)({J}_{2})(J2​) interactions, in a magnetic field. We show that the classical model has an accidental degeneracy for all J2/J1{J}_{2}/{J}_{1}J2​/J1​ and all fields, but the degeneracy is lifted by quantum fluctuations. We show that at large spin SSS, for J2/J1<1/8{J}_{2}/{J}_{1}<1/8J2​/J1​<1/8, quantum fluctuations select the same sequence of three sublattice co-planar states in a field as for J2=0{J}_{2}=0J2​=0, and for 1/8<J2/J1<11/8<{J}_{2}/{J}_{1}<11/8<J2​/J1​<1, they select the canted stripe state for all nonzero fields. The transition between the two states is first order in all fields, with the hysteresis width set by quantum fluctuations. We study the model with arbitrary SSS, including S=1/2S=1/2S=1/2, near the saturation field by exploring the fact that near saturation the density of bosons is small for all SSS. We show that for S>1S>1S>1, the transition remains first order, with a finite hysteresis width, but for S=1/2S=1/2S=1/2 and, possibly, S=1S=1S=1, there appears a new intermediate phase without a quasiclassical long-range order.
We study the S=1S=1S=1 square lattice Heisenberg antiferromagnet with spatially anisotropic nearest-neighbor couplings J1x{J}_{1x}J1x​ and J1y{J}_{1y}J1y​ frustrated by a next-nearest-neighbor coupling J2{J}_{2}J2​ numerically using the density-matrix renormalization-group (DMRG) method and analytically employing the Schwinger-Boson mean-field theory (SBMFT). Up to relatively strong values of the anisotropy, within both methods we find quantum fluctuations to stabilize the N\'eel-ordered state above the classically stable region. Whereas SBMFT suggests a fluctuation-induced first-order transition between the N\'eel state and a stripe antiferromagnet for $1/3\ensuremath{\le}{J}_{1x}/{J}_{1y}\ensuremath{\le}1$ and an intermediate paramagnetic region opening only for very strong anisotropy, the DMRG results clearly demonstrate that the two magnetically ordered phases are separated by a quantum-disordered region for all values of the anisotropy with the remarkable implication that the quantum paramagnetic phase of the spatially isotropic ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model is continuously connected to the limit of decoupled Haldane spin chains. Our findings indicate that for S=1S=1S=1 quantum fluctuations in strongly frustrated antiferromagnets are crucial and not correctly treated on the semiclassical level.
We study the ground-state phase diagram of the spin-1/21/21/2${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model on the square lattice with an accurate bosonic resonating-valence-bond (RVB) wave function. In contrast to the RVB ansatz based on Schwinger fermions, the representation based on Schwinger bosons, supplemented by a variational Monte Carlo technique enforcing the exact projection onto the physical subspace, is able to describe a fully gapped spin liquid in the strongly frustrated regime. In particular, a fully symmetric Z2{Z}_{2}Z2​ spin liquid is stable between two antiferromagnetic phases; a continuous transition at J2=0.4J1{J}_{2}=0.4{J}_{1}J2​=0.4J1​, when the Marshall sign rule begins to be essentially violated, and a first-order transition around J2=0.6J1{J}_{2}=0.6{J}_{1}J2​=0.6J1​ are present. Most importantly, the triplet gap is found to have a nonmonotonic behavior, reaching a maximum around J2=0.51J1{J}_{2}=0.51{J}_{1}J2​=0.51J1​, when the lowest spinon excitation moves from the $\ensuremath{\Gamma}$ to the MMM point, i.e., $k=(\ensuremath{\pi},0)$.