Partha Sarker

---

Frustrated spin systems are a platform for a multitude of exotic physical phenomena. Although models involving frustrated spin interactions have been studied in great detail over the last few decades, the study of frustrated multipolar exchange interaction has only started to gain momentum in recent years. A recent numerical study involving frustrated quadrupolar interaction for $S = 1$ on honeycomb lattice has provided evidence of deconfined phase with $\mathbb{Z}_2$ topological order. The thesis delves extensively into different properties of this quadrupolar spin-$1$ Hamiltonian.

In the absence of exact solution of the frustrated quadrupolar model, we employ several mean field methods to analyze different parameter regimes of the model. We have found that the quadrupolar Hamiltonian has extreme degeneracy by probing it with deformations in the framework of generalized spin wave theory. A formulation of mean field ground states can explain this extensive degeneracy at the isotropic point. Away from the isotropic point, the Hamiltonian does not show any evidence of topological ground state degeneracy. Furthermore, we also analyze the exact symmetries of the model using parton construction showcasing the presence of deconfined excitations. Finally, we employ parton mean field theory to analyze the different phase properties of the model at different parameter regime.

---

University of Cologne
0.03
Contact: Urban Seifert