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The rapid experimental progress of ultra-cold dipolar fermions opens up a whole new opportunity to investigate novel many-body physics of fermions. In this article, we review theoretical studies of the Fermi liquid theory and Cooper pairing…
Disordered magnetic states known as spin liquids are of paramount importance in both fundamental and applied science. A classical state of this kind was predicted for the Ising antiferromagnetic triangular model more than half a century…
The interplay of spin-orbit-coupling and strong electronic correlations is studied for the single-layer and the bilayer compound of the strontium ruthenate Ruddlesden-Popper series by a combination of first-principles band-structure theory…
We show that an unconventional superfluid triggered by spin-orbit coupling is realized for repulsively interacting quasi-one-dimensional fermions. A competition between spin-singlet and -triplet pairings occurs due to the breaking of…
We describe electron spin resonance in a quantum spin liquid with significant spin-orbit coupling. We find that the resonance directly probes spinon continuum which makes it an efficient and informative probe of exotic excitations of the…
For certain crystalline systems, most notably the organic compound EtMe3Sb[Pd(dmit)2]2, experimental evidence has accumulated of an insulating state with a high density of gapless neutral excitations that produce Fermi-liquid-like power…
We study the effective spin-orbital model for honeycomb-layered transition metal compounds, applying the second-order perturbation theory to the three-orbital Hubbard model with the anisotropic hoppings. This model is reduced to the Kitaev…
In this paper, we study the role of both "spin"(species) and mass imbalance in a mixture of two species of fermionic atoms with attractive interaction in an one-dimensional optical lattice. Using the bosonization approach, quantum phase…
A Fermi-liquid (FL) with spin-orbit coupling (SOC) supports a special type of collective modes--chiral spin waves--which are oscillations of magnetization even in the absence of the external magnetic field. We study the chiral spin waves of…
Chiral spin liquids (CSLs) are exotic phases of interacting spins in two dimensions, characterized by long-range entanglement and fractional excitations. We construct a local Hamiltonian on the triangular lattice that stabilizes the…
We present a first-principle study of spin-orbit coupling effects on the Fermi surface of Sr2RuO4 and Sr2RhO4. For nearly degenerate bands, spin-orbit coupling leads to a dramatic change of the Fermi surface with respect to non-relativistic…
We use a projective symmetry group analysis to determine all symmetric spin liquids on the stuffed honeycomb lattice Heisenberg model. This lattice interpolates between honeycomb, triangular and dice lattices, always preserving hexagonal…
We investigate the stability and the nature of the chiral spin liquids which were recently uncovered in extended Heisenberg models on the kagome lattice. Using a Gutzwiller projected wave function approach -- i.e. a parton construction --…
The spin Hall effect is investigated in a two-orbital tight-binding model on a honeycomb lattice. We show that the model exhibits three topologically-different insulating phases at half filling, which are distinguished by different…
Spin-orbit coupling plays an important role in determining the properties of solids, and is crucial for spintronics device applications. Conventional spin-orbit coupling arises microscopically from relativistic effects described by the…
We performed an exact diagonalization study of the spin liquid phase of the Multiple-Spin Exchange model on the triangular lattice. It is characterized by no Neel Long Range Order (NLRO), short-ranged magnetic correlations and a spin gap.…
The discovery of correlated insulating states in moir\'e heterostructures has renewed the interest in strongly-coupled electron systems where spin and valley (or layer) degrees of freedom are intertwined. In the strong-coupling limit, such…
We established a large class of exactly soluble spin liquids and chiral spin liquids on three dimensional helix lattices by introducing Kitaev-type's spin coupling. In the chiral spin liquids, exact stable ground states with spontaneous…
Recently, a number of experiments indicate the possible presence of spin liquid phases in quantum magnets with spin-1/2 and spin-1 moments sitting on triangular-lattice-based structures in Ba3CuSb2O9 and Ba3NiSb2O9 respectively. In relation…
It is commonly believed that strongly interacting one-dimensional Fermi systems with gapless excitations are effectively described by Luttinger liquid theory. However, when the temperature of the system is high compared to the spin energy,…