Alladi Ramakrishnan Hall

Investigations into Quantum Compass Models in Two Dimensions.

Mr Soumya Sur

IMSc

Quantum many-body systems with competing interactions are found to be potential candidates exhibiting unconventionally ordered phases and fractionalized excitations. The exactly solvable Kitaev’s 2D spin model has incited intense activity in this direction. In this talk, I present our investigations on quantum compass models (QCMs) on the square and honeycomb lattices. The motivation for studying QCM stems from its unusual symmetries and applications to various physical situations, from real materials to various engineered platforms. On the square lattice, we develop a novel mean-field approach that respects the stringent constraints set by the "gauge-like" symmetries and self-duality. We find excellent agreement with ab-initio numerical studies (PCUT, PEPS), showing a first-order quantum phase transition (QPT) separating two dual, Ising nematic phases. Next, we discuss our work on the QCM on a honeycomb lattice. By exploiting various duality relations, we uncover a 3D Ising universality as well as a second-order QPT separating a higher-order, symmetry-protected topological superfluid and a Mott insulator having topological order. A closely related fermionic compass-Hubbard model is then studied using two complementary methods: (a) a two-particle self-consistent approach and (b) a strong-coupling perturbation theory to study its various weak and strong-coupling phases. We observe a temperature-dependent dimensional crossover, from a high-T quasi-1d Luttinger liquid-like phase (with power law behavior in the self-energy) to a 2d Ising spin-density wave phase with a low-energy pseudo-gap, which mainly stems from the exact low-dimensional symmetries embedded in this model. Advances in the synthesis of novel spin-orbit coupled insulators, along with advancements in cold atom technologies, could potentially make it possible to achieve these states of matter in the near future.