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The spin-1/2 and spin-1 quantum $J_1$--$J'_1$--$J_2$ Heisenberg models on the square lattics

R. F. Bishop, P. H. Y. Li, R. Darradi, Johannes Richter

Published Jan 1, 2008• 0 citations
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The spin-1/2 and spin-1 quantum J1J_1J1​--J1′J'_1J1′​--J2J_2J2​ Heisenberg models on the square lattics
The spin-1/21/21/2 J1−J2J_1-J_2J1​−J2​ Heisenberg antiferromagnet on a square lattice:a plaquette renormalized tensor network study
We studied the ground-state phase diagram of spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model on the square lattice with first-neighbor J1{J}_{1}J1​ and second-neighbor J2{J}_{2}J2​ antiferromagnetic interactions using both infinite density matrix renormalization group (iDMRG) and DMRG approaches. We show that a plaquette valence bond phase is realized in an intermediate region $0.50\ensuremath{\le}{J}_{2}/{J}_{1}<0.54$ between a N\'eel magnetic ordered phase at J2/J1<0.50{J}_{2}/{J}_{1}<0.50J2​/J1​<0.50 and a stripy magnetic ordered phase at ${J}_{2}/{J}_{1}\ensuremath{\ge}0.54$. The plaquette valence bond phase is characterized by finite dimer orders in both the horizontal and vertical directions. Contrary to the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model, we do not find numerical evidence for a quantum spin liquid phase in the ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model.