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arXiv:1209.6091 · Physical Review B

Plaquette resonating valence bond state in a frustrated honeycomb antiferromagnet

R. Ganesh, Satoshi Nishimoto, Jeroen van den Brink

Published Feb 13, 2013• 26 citations
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Abstract

We study the proposed plaquette resonating valence bond (pRVB) state in the honeycomb lattice ${J}_{1}\ensuremath{-}{J}_{2}$ model with frustration arising from next-nearest-neighbor interactions. Starting with the limit of decoupled hexagons, we develop a plaquette operator approach to describe the pRVB state and its low-energy excitations. Our calculation clarifies that the putative pRVB state necessarily has $f$-wave symmetry: the plaquette wave function is an antisymmetric combination of the Kekul\'e structures. We estimate the plaquette ordering amplitude, ground-state energy, and spin gap as a function of ${J}_{2}/{J}_{1}$. The pRVB state is most stable around ${J}_{2}/{J}_{1}\ensuremath{\sim}0.25$. We identify the wave vectors of the lowest triplet excitations, which can be verified using exact diagonalization or density-matrix renormalization group (DMRG) studies. When ${J}_{2}$ is reduced, we can have either a deconfined quantum phase transition (QPT) or a first-order transition into a N\'eel state. When ${J}_{2}$ is increased, we surmise that the system will undergo a first-order phase transition into a state which breaks lattice rotational symmetry.

DOI
10.1103/physrevb.87.054413

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We study the proposed plaquette resonating valence bond (pRVB) state in the honeycomb lattice J1\ensuremath−J2{J}_{1}\ensuremath{-}{J}_{2}J1​\ensuremath−J2​ model with frustration arising from next-nearest-neighbor interactions. Starting with the limit of decoupled hexagons, we develop a plaquette operator approach to describe the pRVB state and its low-energy excitations. Our calculation clarifies that the putative pRVB state necessarily has fff-wave symmetry: the plaquette wave function is an antisymmetric combination of the Kekul'e structures. We estimate the plaquette ordering amplitude, ground-state energy, and spin gap as a function of J2/J1{J}_{2}/{J}_{1}J2​/J1​. The pRVB state is most stable around J2/J1\ensuremath∼0.25{J}_{2}/{J}_{1}\ensuremath{\sim}0.25J2​/J1​\ensuremath∼0.25. We identify the wave vectors of the lowest triplet excitations, which can be verified using exact diagonalization or density-matrix renormalization group (DMRG) studies. When J2{J}_{2}J2​ is reduced, we can have either a deconfined quantum phase transition (QPT) or a first-order transition into a N'eel state. When J2{J}_{2}J2​ is increased, we surmise that the system will undergo a first-order phase transition into a state which breaks lattice rotational symmetry.
We study the ground-state (gs) phase diagram of the frustrated spin-12\frac{1}{2}21​ J1{J}_{1}J1​--J2{J}_{2}J2​--J3{J}_{3}J3​ antiferromagnet with ${J}_{2}={J}_{3}=\ensuremath{\kappa}{J}_{1}$ on the honeycomb lattice using coupled-cluster theory and exact diagonalization methods. We present results for the gs energy, magnetic order parameter, spin-spin correlation function, and plaquette valence-bond crystal (PVBC) susceptibility. We find a N\'eel antiferromagnetic (AFM) phase for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}\ensuremath{\approx}0.47$, a collinear striped AFM phase for $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}\ensuremath{\approx}0.60$, and a paramagnetic PVBC phase for ${\ensuremath{\kappa}}_{{c}_{1}}\ensuremath{\lesssim}\ensuremath{\kappa}\ensuremath{\lesssim}{\ensuremath{\kappa}}_{{c}_{2}}$. The transition at ${\ensuremath{\kappa}}_{{c}_{2}}$ appears to be of first-order type, while that at ${\ensuremath{\kappa}}_{{c}_{1}}$ is continuous. Since the N\'eel and PVBC phases break different symmetries our results favor the deconfinement scenario for the transition at ${\ensuremath{\kappa}}_{{c}_{1}}$.
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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.
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