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arXiv:cond-mat/9312059 · Modern Physics Letters B

OPTIMIZING THE RVB STATE ON A TRIANGULAR LATTICE: PRESENCE OF THE LONG RANGE ORDER

Yong-Cong Chen

Published Aug 30, 1994• 6 citations
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Abstract

We present a Schwinger boson approach for the RVB state of the spin-1/2 Heisenberg antiferromagnet on a triangular lattice. It is shown that a Gutzwiller projection of the mean field state that includes both antiferromagnetic and ferromagnetic decouplings leads to optimizing the RVB pair amplitudes within a self-consistent approximation. The resulting state yields, by Monte Carlo simulations, energies and spin-spin correlations in excellent agreement with the exact diagonalization result on finite lattices (up to 36 sites). We conclude that the optimized RVB wave function possesses a long range three-sublattice order.

DOI
10.1142/s0217984994001242

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The spin-1/2 antiferromagnetic Heisenberg and X Y models are investigated on the triangular lattice by numerically diagonalizing finite size systems (up to 21 spins). The ground state energies of both models are found to be close to other theoretical predictions except those of Marland and Betts who performed similar analysis to ours. We have numerically constructed a resonating valence bond state of Anderson. It has a relatively large projection on the ground state of the finite Heisenberg model, although the absolute value of the projection decreases linearly with the system size. The trial function proposed by Miyashita for the X Y model does not have an appreciable projection on the numerically exact state. We present evidence for the absence of a sublattice long range order in the Heisenberg model and the existence of the same quantity in the X Y model.

Journal of the Physical Society of Japan•Jan 15, 1986•79 citations
We present a Schwinger boson approach for the RVB state of the spin-1/2 Heisenberg antiferromagnet on a triangular lattice. It is shown that a Gutzwiller projection of the mean field state that includes both antiferromagnetic and ferromagnetic decouplings leads to optimizing the RVB pair amplitudes within a self-consistent approximation. The resulting state yields, by Monte Carlo simulations, energies and spin-spin correlations in excellent agreement with the exact diagonalization result on finite lattices (up to 36 sites). We conclude that the optimized RVB wave function possesses a long range three-sublattice order.
Through Variational Monte Carlo simulation we show the d-wave RVB pairing in the Heisenberg model on triangular lattice can be better described in terms of a two component order parameter. The fully gapped chiral d-wave RVB state, which is predicted by the mean field theory to be the unique minimum of variational energy in the two dimensional representation space of d-wave pairing, is found to be actually a local maximum and the true minimum of energy is reached by the non-chiral dxyd_{xy}dxy​ state with line nodes. We also find that the usual Gutzwiller approximation, which enjoys great success for the square lattice system, fails badly on the triangular lattice as a result of the geometric frustration inherent of the system. An improved version of the Gutzwiiler approximation is proposed and is found to give a much better results than the usual one.
'Resonating-valence-bond' (RVB) variational wavefunctions are numerically investigated in order to describe the ground state and the singlet low-lying excited states of the spin-1/2, J 1 -J 2 Heisenberg antiferromagnet with 1/8<or approximately=J 2 /J 1 <or approximately=1 on triangular lattices of N=4p sites compatible with the classical Neel orders. Comparison with previous exact diagonalization results indicates that the singlet eigenstates associated with collinear Neel order, among which the ground state is found, can be accurately described with appropriate superpositions of two-sublattice RVB trial states, while the other singlet low-lying eigenstates associated with four-sublattice Neel order can be well approximated from the four-sublattice RVB trial states.
We investigate the spin dynamics of the square-lattice spin- 1/2 Heisenberg antiferromagnet by means of an improved mean-field Schwinger boson calculation. By identifying both, the long-range Neel and the RVB-like components of the ground state, we propose an educated guess for the mean-field magnetic excitation consisting on a linear combination of local and bond spin flips to compute the dynamical structure factor. Our main result is that when this magnetic excitation is optimized in such a way that the corresponding sum rule is fulfilled, we recover the low- and high-energy spectral weight features of the experimental spectrum. In particular, the anomalous spectral weight depletion at (π, 0) found in recent inelastic neutron scattering experiments can be attributed to the interference of the triplet bond excitations of the RVB component of the ground state. We conclude that the Schwinger boson theory seems to be a good candidate to adequately interpret the dynamic properties of the square-lattice Heisenberg antiferromagnet.
We investigate the spin dynamics of the square-lattice spin- Heisenberg antiferromagnet by means of an improved mean-field Schwinger boson calculation. By identifying both, the long-range Néel and the RVB-like components of the ground state, we propose an educated guess for the mean-field magnetic excitation consisting on a linear combination of local and bond spin flips to compute the dynamical structure factor. Our main result is that when this magnetic excitation is optimized in such a way that the corresponding sum rule is fulfilled, we recover the low- and high-energy spectral weight features of the experimental spectrum. In particular, the anomalous spectral weight depletion at found in recent inelastic neutron scattering experiments can be attributed to the interference of the triplet bond excitations of the RVB component of the ground state. We conclude that the Schwinger boson theory seems to be a good candidate to adequately interpret the dynamic properties of the square-lattice Heisenberg antiferromagnet.
We study the ground state phase diagram of the bilayer Heisenberg model on a square lattice with a bosonic resonating valence bond (RVB) wavefunction. The wavefunction has the form of a Gutzwiller projected Schwinger boson mean-field ground state and involves two variational parameters. We find the wavefunction provides an accurate description of the system on both sides of the quantum phase transition. In particular, through the analysis of the spin structure factor, ground state fidelity susceptibility and the Binder moment ratio Q(2), a continuous transition from the antiferromagnetic ordered state to the quantum disordered state is found at the critical coupling of α(c) = J(⊥)/J(∥) ≈ 2.62, in good agreement with the result of quantum Monte Carlo simulation. The critical exponent estimated from the finite size scaling analysis (1/ν ≈ 1.4) is consistent with that of the classical 3D Heisenberg universality class.
The spin-1/2 antiferromagnetic Heisenberg and X Y models are investigated on the triangular lattice by numerically diagonalizing finite size systems (up to 21 spins). The ground state energies of both models are found to be close to other theoretical predictions except those of Marland and Betts who performed similar analysis to ours. We have numerically constructed a resonating valence bond state of Anderson. It has a relatively large projection on the ground state of the finite Heisenberg model, although the absolute value of the projection decreases linearly with the system size. The trial function proposed by Miyashita for the X Y model does not have an appreciable projection on the numerically exact state. We present evidence for the absence of a sublattice long range order in the Heisenberg model and the existence of the same quantity in the X Y model.