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arXiv · 1802.00874

Quantum phase diagram of spin-$1$ $J_1-J_2$ Heisenberg model on the square lattice: an infinite projected entangled-pair state and density matrix renormalization group study

R. Haghshenas·Wang-Wei Lan·Shou-Shu Gong·D. N. Sheng
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Abstract

We study the spin-$1$ Heisenberg model on the square lattice with the antiferromagnetic nearest-neighbor $J_1$ and the next-nearest-neighbor $J_2$ couplings by using the infinite projected entangled-pair state (iPEPS) ansatz and density matrix renormalization group (DMRG) calculation. The iPEPS simulation, which studies the model directly in the thermodynamic limit, finds a crossing of the ground state from the Néel magnetic state to the stripe magnetic state at $J_2/J_1 \simeq 0.549$, showing a direct phase transition. In the finite-size DMRG calculation on the cylinder geometry up to the cylinder width $L_y = 10$, we find a very small intermediate regime $\sim 0.005 J_1$ between the two magnetic order phases, which may imply the absent intermediate phase. Both calculations identify that the stripe order comes with a first-order transition at $J_2/J_1 \simeq 0.549$. Our results indicate that unlike the spin-$1/2$ $J_1-J_2$ square model, quantum fluctuations in the spin-$1$ model may be not strong enough to stabilize an intermediate non-magnetic phase.

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R. Haghshenas, Wang-Wei Lan, Shou-Shu Gong, D. N. Sheng. 2018-05-31. Quantum phase diagram of spin-$1$ $J_1-J_2$ Heisenberg model on the square lattice: an infinite projected entangled-pair state and density matrix renormalization group study. https://doi.org/10.1103/physrevb.97.184436

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