# Low-energy singlet sector in the spin-1/2 J1–J2 Heisenberg model on a square lattice

@article{Aktersky2016LowenergySS,
title={Low-energy singlet sector in the spin-1/2 J1–J2 Heisenberg model on a square lattice},
author={A.Yu. Aktersky and A. V. Syromyatnikov},
journal={Journal of Experimental and Theoretical Physics},
year={2016},
volume={123},
pages={1035-1042}
}
• Published 17 May 2016
• Physics
• Journal of Experimental and Theoretical Physics
Based on a special variant of the plaquette expansion, an operator is constructed whose eigenvalues give the low-energy singlet spectrum of a spin-$$\frac{1}{2}$$12 Heisenberg antiferromagnet on a square lattice with nearest-heighbor and frustrating next-nearest-neighbor exchange couplings J1 and J2. It is well known that a nonmagnetic phase arises in this model for 0.4 ≲ J2/J1 ≲ 0.6, sandwiched by two Néel ordered phases. In agreement with previous results, we observe a first-order quantum…
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## References

SHOWING 1-10 OF 29 REFERENCES
Quantum Spin Liquid in Spin 1/2 J1–J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
• Physics
• 2014
The nature of quantum spin liquids is studied for the spin-1/2 antiferromagnetic Heisenberg model on a square lattice containing exchange interactions between nearest-neighbor sites, J1, and those
The spin-1/2 J1–J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• Physics
• 2010
AbstractWe present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square lattices of up to N=40 sites. Using
Spin-(1)/(2) J 1 -J 2 Heisenberg antiferromagnet on a square lattice: A plaquette renormalized tensor network study
• Physics
• 2012
We apply the plaquette renormalization scheme of tensor network states [Phys. Rev. E, 83, 056703 (2011)] to study the spin-1/2 frustrated Heisenberg J1-J2 model on a L*L square lattice with L = 8, 16
Plaquette ordered phase and quantum phase diagram in the spin-1/2 J(1)-J(2) square Heisenberg model.
• Physics
Physical review letters
• 2014
We study the spin-1/2 Heisenberg model on the square lattice with first- and second-neighbor antiferromagnetic interactions J(1) and J(2), which possesses a nonmagnetic region that has been debated
Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Physics
• 2011
We perform highly accurate density matrix renormalization group (DMRG) simulations to investigate the ground state properties of the spin-1/2 antiferromagnetic square lattice Heisenberg $J_1$-$J_2$
Hierarchical mean-field approach to the J 1 -J 2 Heisenberg model on a square lattice
• Physics
• 2009
We study the quantum phase diagram and excitation spectrum of the frustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of
Dimer order with striped correlations in the J 1 -J 2 Heisenberg model
• Physics
• 1999
Ground state energies for plaquette and dimer order in the $J_1-J_2$ square-lattice spin-half Heisenberg model are compared using series expansion methods. We find that these energies are remarkably
The spin-1/2 square-lattice J1-J2 model: the spin-gap issue
• Physics
• 2014
We use the coupled cluster method to high orders of approximation in order to calculate the ground-state energy, the ground-state magnetic order parameter, and the spin gap of the spin-1/2 J1-J2
J 1 -J 2 frustrated two-dimensional Heisenberg model: Random phase approximation and functional renormalization group
• Physics
• 2010
We study the ground-state properties of the two-dimensional spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on a square lattice, within diagrammatic approximations using an