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We study the magnetic ordered phases of the spin-1/2 Heisenberg antiferromagnetic model with nearest J1 and next nearest neighbor J2 exchange interactions on the square lattice using fermionic representation of spin operators within Popov-Fedotov approach.The unphysical states are eliminated on each site by introducing an imaginary chemical potential. Working in local coordinate system for every site we investigate the different ordered phases in dependence on exchange parameters. At T = 0 we recover the conventional spin wave results. | Communications in Physics, Vol. 24, No. 3 (2014), pp. 193-200 DOI:10.15625/0868-3166/24/3/5027 MAGNETIC PROPERTIES OF QUANTUM SQUARE LATTICE HEISENBERG ANTIFERROMAGNET WITH FRUSTRATION: AN AUXILIARY FERMION APPROACH PHAM THI THANH NGA Water Resources University, 175 Tay Son, Hanoi NGUYEN TOAN THANG Institute of Physics, Vietnam Academy of Science and Technology E-mail: nga ptt@wru.edu.vn Received 17 May 2014 Accepted for publication 22 July 2014 Abstract. We study the magnetic ordered phases of the spin-1/2 Heisenberg antiferromagnetic model with nearest J1 and next nearest neighbor J2 exchange interactions on the square lattice using fermionic representation of spin operators within Popov-Fedotov approach.The unphysical states are eliminated on each site by introducing an imaginary chemical potential. Working in local coordinate system for every site we investigate the different ordered phases in dependence on exchange parameters. At T = 0 we recover the conventional spin wave results. Keywords: functional integral, antiferromagnetic Heisenberg model, square lattice, frustration. I. INTRODUCTION Recently, geometric frustration in spin systems has attracted a lot of interest. The discovery of the ceramic high-temperature superconductivity has stimulated great interests in studying possible novel phases in frustrated quantum antiferromagnet on two-dimensional lattices [1]. The square lattice antiferromagnetic Heisenberg model with frustration introduced by next nearest neighbor exchange interaction has been investigated by many authors with various approximate and numerical methods: the spin wave theory [2, 3]; small lattice calculations [4]; the Schwinger boson theory [5]; series expansion [6] and other methods [7]. However, there is a considerable discrepancy between the results of above works, in particular for the ground state properties of the system. The reason is the complex nature of spin operators. The non - canonical commutation relations of spin .
