The Heart of Entanglement:

Chiral, Nematic, and Incommensurate Phases in the Kitaev-Gamma Ladder in a Field: The bond-dependent Kitaev model on the honeycomb lattice with anyonic excitations has recently attracted considerable attention. However, in solid state materials other spin interactions are present, and among such additional interactions, the off-diagonal symmetric Gamma interaction, another type of bond-dependent term, has been particularly challenging to fully understand. A minimal Kitaev-Gamma (KG) model has been investigated by various numerical techniques under a magnetic field, but definite conclusions about field-induced spin liquids remain elusive and one reason may lie in the limited sizes of the two-dimensional geometry it is possible to access numerically. We therefore focus on the KG model defined on a two-leg ladder which is much more amenable to a complete study, and determine the entire phase diagram in the presence of a magnetic field along [111]-direction. Due to the competition between the interactions and the field, an extremely rich phase diagram emerges with fifteen distinct phases. Focusing near the antiferromagnetic Kitaev region, we identify nine different phases solely within this region: several incommensurate magnetically ordered phases, spin nematic, and two chiral phases with enhanced entanglement. Of particular interest is a highly entangled phase with staggered chirality with zero-net flux occurring at intermediate field, which along with its companion phases outline a heart-shaped region of high entanglement, the heart of entanglement. We compare our results for the ladder with a C3 symmetric cluster of the two-dimensional honeycomb lattice, and offer insights into possible spin liquids in the two-dimensional limit. Check here for details.

Higher-spin Kitaev model:

The spin S=12 Kitaev honeycomb model has attracted significant attention, since emerging candidate materials have provided a playground to test non-Abelian anyons. The Kitaev model with higher spins has also been theoretically studied, as it may offer another path to a quantum spin liquid. However, a microscopic route to achieve higher spin Kitaev models in solid state materials has not been rigorously derived. Here we present a theory of the spin S=1 Kitaev interaction in two-dimensional edge-shared octahedral systems. Essential ingredients are strong spin-orbit coupling in anions and strong Hund’s coupling in transition metal cations. The S=1 Kitaev and ferromagnetic Heisenberg interactions are generated from superexchange paths. Taking into account the antiferromagnetic Heisenberg term from direct-exchange paths, the Kitaev interaction dominates the physics of S=1 system. Using exact diagonalization technique, we show a finite regime of S=1 spin liquid in the presence of the Heisenberg interaction. Candidate materials are proposed, and generalization to higher spins is discussed here.

Spin-Orbit Physics:

Recently, the effects of spin-orbit coupling (SOC) in correlated materials have become one of the most actively studied subjects in condensed matter physics, as correlations and SOC together can lead to the discovery of new phases. Among candidate materials, iridium oxides (iridates) have been an excellent playground to uncover such novel phenomena. In this review, we discuss recent progress in iridates and related materials, focusing on the basic concepts, relevant microscopic Hamiltonians, and unusual properties of iridates in perovskite- and honeycomb-based structures. Perspectives on SOC and correlation physics beyond iridates are also discussed here.

Electronic Nematic Liquid:

Electrons in solids are either localized near host atoms or move freely to account for metallic behaviour. In correlated materials, electrons can self-assemble themselves in states that analogous to classical liquid crystal phases. The search for such phases in solid-state systems, in particular for the quantum version of an anisotropic liquid crystal, dubbed electronic nematic phase, has been of great interest. Such a phase spontaneously breaks the point-group symmetry of the underlying lattice thus characteristically modifying, e.g., transport properties. A variety of transition metal materials such as Cooper-, Ruthenium-based oxides and Iron Pnictides has been proposed to harbour an electronic nematic phase. We have extensively worked on interplay between orbitals and spins to understand microscopic mechanism of electronic nematic phases and associated phenomena. See our papers on arXiv.org (under publication).