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Quantum spin liquids (QSLs) represent exotic states of matter where quantum spins interact strongly yet evade long-range magnetic order down to absolute zero. Characterized by non-local quantum entanglement and resultant fractionalized…
Due to the combination of a substantial spin-orbit coupling and correlation effects, iridium oxides hold a prominent place in the search for novel quantum states of matter, including, e.g., Kitaev spin liquids and topological Weyl states.…
We study the effective low-energy fermionic theory of the Kondo-Kitaev model to leading order in the Kondo coupling. Our main goal is to understand the nature of the superconducting instability induced in the proximate metal due to its…
We report the synthesis and properties of (H,Li)$_{6}$Ru$_{2}$O$_{6}$, which is shown to be a $J_{\text{eff}}=\frac{1}{2}$ system made out of Ru$^{3+}$ moments in a honeycomb geometry. Bulk magnetization, heat capacity, nuclear magnetic…
In the quest for realizations of quantum spin liquids, the exploration of Kitaev materials - spin-orbit entangled Mott insulators with strong bond-directional exchanges - has taken center stage. However, in these materials the local…
Na$_2$IrO$_3$, a honeycomb 5$d^5$ oxide, has been recently identified as a potential realization of the Kitaev spin lattice. The basic feature of this spin model is that for each of the three metal-metal links emerging out of a metal site,…
We investigate the half-filled Hubbard model on an isotropic triangular lattice with the variational cluster approximation. By decreasing the on-site repulsion $U$ (or equivalently increasing pressure) we go from a phase with long range,…
Quantum spin models with spatially dependent interactions, known as compass models, play an important role in the study of frustrated quantum magnetism. One example is the Kitaev model on the honeycomb lattice with spin-liquid ground states…
Compounds of transition metal ions with strong spin-orbit coupling recently attracted attention due to the possibility to host frustrated bond-dependent anisotropic magnetic interactions. In general, such interactions lead to complex phase…
Recent proposals for spin-1 Kitaev materials, such as honeycomb Ni oxides with heavy elements of Bi and Sb, have shown that these compounds naturally give rise to antiferromagnetic (AFM) Kitaev couplings. Conceptual interest in such AFM…
We present an augmented parton mean-field theory which (i) reproduces the $exact$ ground state, spectrum, and dynamics of the quantum spin liquid phase of Kitaev's honeycomb model; and (ii) is amenable to the inclusion of integrability…
Co$^{2+}$ ions in an octahedral crystal field, stabilise a j$_{eff}$ = 1/2 ground state with an orbital degree of freedom and have been recently put forward for realising Kitaev interactions, a prediction we have tested by investigating…
The exactly solvable spin-1/2 Kitaev model on a honeycomb lattice has drawn significant interest, as it offers a pathway to realizing the long-sought after quantum spin liquid. Building upon the Kitaev model, Yao and Lee introduced another…
We analyze the Physics of cold atoms in honeycomb optical lattices with on-site repulsion and spin-orbit couplings that break time reversal symmetry. Such systems, at half filling and large on-site repulsion, have been proposed as a…
We study the spin-$1/2$ Heisenberg model on the square lattice with the first and second nearest-neighbor antiferromagnetic couplings $J_1$, $J_2$, as well as the three-spin scalar chiral coupling $J_{\chi}$. Using density matrix…
We present numerical evidence for the presence of a finite-temperature ($T$) phase transition separating paramagnet and quantum spin liquid in a three-dimensional variant of the Kitaev model defined on a hyperhoneycomb lattice in the limit…
We show that the decorated honeycomb lattice supports a number of topological insulating phases with a non-trivial Z_2 invariant and time-reversal symmetry protected gapless edge modes. We investigate the stability of these phases with…
The Kitaev spin liquid provides a rare example of well-established quantum spin liquids in more than one dimension. It is obtained as the exact ground state of the Kitaev spin model with bond-dependent anisotropic interactions. The peculiar…
This paper reviews the current progress on searching the Kitaev spin liquid state in 3d electron systems. Honeycomb cobaltates were recently proposed as promising candidates to realize the Kitaev spin liquid state, due to the more localized…
Spin systems with frustrated anisotropic interactions are of significant interest due to possible exotic ground states. We have explored their phase diagram on a nearest-neighbor triangular lattice using the density-matrix renormalization…