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arXiv:1101.0193 · Europhysics Letters (EPL)

Antiferromagnetic long-range order in the uniform resonating valence bond state on the square lattice

Tao Li

Published Sep 1, 2013• 6 citations
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Abstract

With an extensive variational Monte Carlo simulation, we show that the uniform resonating valence bond (U-RVB) state on the square lattice is antiferromagnetic long-range ordered. The ordered moment is estimated to be . Such a behavior is quite unexpected from the slave boson mean-field treatment or the Gutzwiller approximation of the uniform RVB state.

DOI
10.1209/0295-5075/103/57002

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With an extensive variational Monte Carlo simulation, we show that the uniform resonating valence bond (U-RVB) state on the square lattice is antiferromagnetic long-range ordered. The ordered moment is estimated to be . Such a behavior is quite unexpected from the slave boson mean-field treatment or the Gutzwiller approximation of the uniform RVB state.
A two-dimensional square-lattice Hubbard model is investigated. A slave-fermion formulation, in which the electron operator is expressed by a combination of bose operators for the spin freedom, and fermi operators for the charge freedom, is used. The phase diagram for the resonating valence bond (RVB) state is obtained. The RVB state shows long-range antiferromagnetic order at T =0, the period of which deviates from that of the commensurate Néel order as the system deviates from the half-filled case.
In this work, a long-range resonating valence bond state is proposed as a variational wave function for the ground state of the S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg model on the honeycomb lattice. Employing Variational Monte Carlo (VMC) method, we show that the ground state energy obtained from such RVB wave function, lies well below the energy of the Néel state and compares very well to the energies evaluated from spin-wave theory and series expansion method. We also obtain the spin-spin correlation function along zig-zag and armchair directions and find that the two correlations are different, which indicates the anisotropic nature of the system. We compare our results with the square lattice and we show that although the quantum fluctuations on honeycomb lattice are much stronger, but do not completely destroy the magnetic order.
We derive the singlet versions of the N\'eel states for certain n-sublattice systems, including the two-dimensional square lattice (previously considered by Carlson and Sethna) and the triangular lattice. These states are written explicitly in resonating-valence-bond form through the help of the Young-tableau formalism. Since these states are exact ground states for infinite-range models, they can be used as a test for the fermion and Schwinger boson mean-field theories (MFT). We show that the fermion MFT is incompatible with the ground state, while the boson MFT gives the exact ground state. Implications of the results with respect to the ability of the MFT's to describe antiferromagnetic long-range order are discussed.
The ground-state properties of the spin-(1/2 Heisenberg antiferromagnet on a square lattice are studied by using a simple variational wave function that interpolates continuously between the N\'eel state and short-range resonating-valence-bond states. Exact calculations of the variational energy for small systems show that the state with the lowest energy has long-range antiferromagnetic order. The staggered magnetization in this state is approximately 70% of its maximum possible value. The variational estimate of the ground-state energy is substantially lower than the value obtained for the nearest-neighbor resonating-valence-bond wave function.