Master's defense: Qiyu Liu

A study of the J1 -J2 Quantum Heisenberg Antiferromagnets

In this thesis, we formulated the J1-J2 Heisenberg Hamiltonian in terms of the pesudofermion, in which a exact constraint of single occupancy for each site is imposed through the Popov-Fedotov procedure [1]. We have also introduced a more generalized approach to apply the Hubbard-Stratonovich transformation, which enables the decoupling of the Hamiltonian with an interaction matrix that is not positive definite. The investigation of the ground state magnetic properties and low-energy excitations has been conducted within the framework of the path integral formalism. Additionally, an effective field theory is proposed for determining the critical temperature of the nematic phase of J1-J2 Heisenberg model.

[1]: V. N. Popov S. A. Fedotov. The functional-integration method and diagram technique for spin systems. Sov. Phys. JETP, 67(3), March 1988.