Low-dimensional quantum spin systems display intriguing ground state properties , which may have important consequences for the existence of fractionalized excitations or the emergence of high-temperature superconductivity . In this thesis we consider the material in two dimensions which they can be good candidates of existence spin liquid phases . Among various materials that show promising low-temperature behaviors , the family of organic charge transfer salts k-(ET) 2 X (with the anisotropic triangul lattice) , InCu 2/3 V 1/3 O 3 $ , Bi 3 Mn 4 O 12 (NO 3 )(BMNO) and Cu 3 Ni 2 SbO 6 (with the honeycomb lattice) represent a very important candidate for hosting spin-liquid properties . So we study these compounds with two different techniques : 1 - Quantum variational Monte Carlo for transfer salts and 2 - Modified spin wave for other compounds that they are mentioned above. 1 - By using variational wave functions and quantum Monte Carlo techniques , we investigate the complete phase diagram of the Heisenberg model on the anisotropic triangular lattice , where two out of three bonds have superexchange couplings J and the third one has instead J’ This model interpolates between the square lattice and the isotropic triangular one , for J’/J 1 , and between the isotropic triangular lattice and a set of decoupled chains , for J/J’ 1. We consider all the fully symmetric spin liquids that can be constructed with the fermionic projective-symmetry group justify; MARGIN: 0cm 0cm 0pt" 2 - Using modified spin wave (MSW) method , we study the J 1 -J 2 Heisenberg model with first and second neighbor antiferromagnetic exchange interactions . For symmetric S=1/2 model , with the same couplings for all the equivalent neighbors , we find three phase in terms of frustration parameter: (1) a commensurate collinear ordering with staggered magnetization (Neel.I state) , (2) a magnetically gapped disordered state, preserving all the symmetries of the Hamiltonian and lattice , hence by definition is a quantum spin liquid (QSL) state and (3) a commensurate collinear ordering in which two out of three nearest neighbor magnetizations are antiparallel and the remaining pair are parallel (Neel.II state) . We also explore the phase diagram of distorted $J 1 -J 2 model with S=1/2 . Distortion is introduced as an inequality of one nearest neighbor coupling with the other two . This yields a richer phase diagram by the appearance of a new gapped QSL , a gapless QSL and also a valence bond crystal (VBC) phase in addition to the previously three phases found for undistorted model .