Willian Natori: New venues for quantum spin-orbital liquids
Quantum spin liquids (QSL) are exemplars of highly entangled states in the context of strongly correlated spin systems Savary and Balents [6]. A renewed interest for QSLs has been observed in the past few years thanks to the synthesis of new QSL candidates and the improvement of theoretical techniques to their analysis. These two factors are clearly exemplified by the ongoing studies of the Kitaev model on the honeycomb lattice Kitaev [2]. This j = 1=2 spin model displays bond-directional spin interactions that ensure a macroscopic number of conserved quantities. Its ground state is demonstrably a QSL that displays Majorana fermions and a static Z2 gauge field. Moreover, the Kitaev model is relevant to Mott insulators with 4/5d5 magnetic ions and precise prescriptions for their geometric structure Jackeli and Khaliullin [1]. Several compounds were synthesized following these rules but there is still no consensus on whether they implement QSL ground states.
An alternative route to QSL states can be realized in compounds that retain orbital degeneracy. The coupling
between spin and orbital fluctuations hinders order formation in both degrees of freedom, thus favoring a quantum spin-orbital liquid (QSOL). In this seminar, I show how spin-orbital models that favor QSOL ground states can be realistically implemented in Mott insulators with 4/5d1 magnetic ions Natori et al. [3, 4, 5]. These systems are described by effective j = 3=2 Hamiltonians that are expressed by pseudospins s and pseudo-orbitals that display the algebra of j = 1=2 operators. The interactions in these models display a bond-dependence that is similar to the observed on the Kitaev model but yet retain continuous symmetries. We show the potential of resonant inelastic x-ray scattering to explore orders and excitations of s and . We also show how the j = 3=2 counterpart of the Kitaev materials implement the SU(4) Heisenberg model. If time allows, we also discuss some unexpected connections between these works and the Mott physics of twisted bilayer graphene Venderbos and Fernandes [7].
[1] G. Jackeli and G. Khaliullin. Mott insulators in the strong spin-orbit coupling limit: from Heisenberg to a quantum compassand Kitaev models. Physical Review Letters, 102(1):017205, 2009. doi:10.1103/PhysRevLett.102.017205.
[2] A. Kitaev. Anyons in an exactly solved model and beyond. Annals of Physics, 321(1):2–111, 2006.[3] W. M. H. Natori, M. Daghofer, and R. G. Pereira. Dynamics of a j = 32 quantum spin liquid. Physical Review B, 96(12):125109, 2017. doi:10.1103/PhysRevB.96.125109.
[4] W. M. H. Natori et al. Chiral spin-orbital liquids with nodal lines. Physical Review Letters, 117(1):017204, 2016. doi:10.1103/PhysRevLett.117.017204.
[5] Willian M. H. Natori, Eric C. Andrade, and Rodrigo G. Pereira. Su(4)-symmetric spin-orbital liquids on the hyperhoneycomblattice. Phys. Rev. B, 98:195113, Nov 2018. doi:10.1103/PhysRevB.98.195113. URLhttps://link.aps.org/doi/10.1103/PhysRevB.98.195113.
[6] Lucile Savary and Leon Balents. Quantum spin liquids: a review. Reports on Progress in Physics, 80(1):016502, 2017.
[7] Jörn W. F. Venderbos and Rafael M. Fernandes. Correlations and electronic order in a two-orbital honeycomb latticemodel for twisted bilayer graphene. Phys. Rev. B, 98:245103, Dec 2018. doi:10.1103/PhysRevB.98.245103. URL https://link.aps.org/doi/10.1103/PhysRevB.98.245103.