Quantum Phase Transitions And Spin Liquid In The Heisenberg Antiferromagnetic System

As simple and intuitive,Heisenberg model is the typical one to describe spin systems,and is applied to the studies of material magnetism for its fair explanation of insulator magnetism,spontaneously magnetization of ferromagnets,and features of antiferromagnets.The model is of great importance in both theoretical physics and numerical calculations.In this thesis,we use iterative method for numerical calculation of low-lying excitations of the Heisenberg antiferromagnetic system.We apply fidelity,state weight,state pattern,spin correlation,level crossing,order parameter,and structure operator for quantum states to study the quantum phase transitions of the system.We analyze the microscopic mechanism of structure operator in the quantum phase transitions under commutative coupling.As the most important result in this work,we use level crossing and dimer operator to obtain the critical points of quantum phase transitions and the region of spin liquid.In the metric of dimensionless parameter g=J2/J1,we find regime g=0.00?0.40 for Neel phase,and g=0.72?0.99 for stripe phase.Spin singlet E2(S=0)and triplet E1(S=1)cross at critical point gcin1=0.49,and overlap at gcin2=0.53.These two critical points separate the intermediate region as three fine parts.We find doubly degenerate spin singlet of low-lying excitations in the region g=0.50?0.52,and show the singlet as spin liquid using dimer operator.We improve numerical iteration algorithm,and apply it to the calculation of twodimensional antiferromagnetic square system.Using our own C program,we obtain the low-lying excitations of the system.We realize the carpet search for state under the normal precision,and pinpoint the target state with high accuracy.