Numerical Studies of Quantum Spin Liquids in Kitaev and Heisenberg Models

Rapid advancement in large-scale numerical simulations for strongly correlated systems has led to great progress
in identifying and characterizing emerging new states of matter in realistic many-body systems in past a few years.
I will report some of exciting advances including the identification of magnetic fields driven quantum spin liquids in the honeycomb Kitaev model and spin liquids in frustrated kagome and triangular lattice Heisenberg models. Based on the state of the art density matrix renormalization group simulations, we show that the non-Abelian chiral spin liquid emerges for the Kitaev model with antiferromagnetic Kitaev interactions, and remains robust up to a critical magnetic field that is an order of magnitude larger than the corresponding critical field for a ferromagnetic Kitaev model signaling the importance of frustration in such systems. Interestingly, an intermediate gapless spin liquid phase emerges with the increase of the magnetic field, which may be relevant to the experimental system RuCl3 under magnetic fields. For spin Heisenberg lattice models, besides previous discovered robust chiral spin liquid and time-reversal invariant spin liquid, we also establish a new chiral gapless spin liquid on triangular lattice J1-J2-J3 model. Furthermore, we explore the nature of different quantum spin liquids for kagome systems in the presence of DM interactions based on the dynamic structure factor simulation, which demonstrates consistency with observations in inelastic neutron scattering measurements of herbertsmithite.