The Ising phase in the J1-J2 Heisenberg Model

Abstract

The two dimensional Heisenberg antiferromagnet on the square lattice with nearest (J1) and next-nearest (J2) neighbor couplings is investigated in the strong frustration regime (J2/J1>1/2). A new effective field theory describing the long wavelength physics of the model is derived from the quantum hamiltonian. The structure of the resulting non linear sigma model allows to recover the known spin wave results in the collinear regime, supports the presence of an Ising phase transition at finite temperature and suggests the possible occurrence of a non-magnetic ground state breaking rotational symmetry. By means of Lanczos diagonalizations we investigate the spin system at T=0, focusing our attention on the region where the collinear order parameter is strongly suppressed by quantum fluctuations and a transition to a non-magnetic state occurs. Correlation functions display a remarkable size independence and allow to identify the transition between the magnetic and non-magnetic region of the phase diagram. The numerical results support the presence of a non-magnetic phase with orientational ordering.

6 pages, 4 figures, to be published in PRB

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• Coupled cluster and perturbation theories based on a cluster mean-field reference applied to strongly correlated spin systems
• The double life of electrons in magnetic iron pnictides, as revealed by NMR
• Symmetry-projected cluster mean-field theory applied to spin systems
• Generalized Phase-Space Techniques to Explore Quantum Phase Transitions in Critical Quantum Spin Systems
• Linear combinations of cluster mean-field states applied to spin systems
• The quantum J_{1}-J_{1'}-J_{2} spin-1/2 Heisenberg antiferromagnet: A variational method study
• Magnetic and transport properties of the one-dimensional ferromagnetic Kondo lattice model with an impurity