Research Scholars Annex Hall

Investigations into Quantum Compass Models in Two Dimensions

Soumya Sur

IMSc

Quantum many-body systems with competing interactions are found as po- tential candidates to host unconventional ordered phases and fractionalized ex- citations. The exactly soluble Kitaev Honeycomb model has incited intense activity in this context. In this talk, we present our investigations on quan- tum compass models (QCM) on the square and honeycomb lattices. Motivation for studying QCM comes from its unusual symmetries and it’s applications in diverse physical platforms, starting from real materials to various engineered platforms. On the square lattice, we develop a novel mean-field theory which respects the stringent constraints set by the “gauge-like” symmetries and self- duality. We find an excellent accord with ab-initio numerical studies (PCUT, PEPS), showing a first-order quantum phase transition (QPT) separating two dual, Ising nematic phases. Qualitative discussion of our results in the con- text of Kugel-Khomskii spin-orbital physics are then made. Next, we discuss the QCM on a honeycomb lattice, where various duality relations uncover a 3d Ising universality, as well as a QPT between a higher-order, topological super- fluid and a Mott insulator having topological order. A closely related fermionic compass-Hubbard model is studied using two complementary methods (a) two- particle self-consistent approach, and (b) strong-coupling perturbation theory to study its various weak and strong coupling phases. Finally, we qualitatively discuss about the implications of an experimentally realizable (in cold-atom se- tups) perturbation on the above strong-coupling phase with the possibility of realizing a Lifshitz type criticality