Numerical studies on the 2d frustrated magnet

Abstract

Neighboring spins in a magnetic material interact in various ways and arrange themselves to minimize their interaction energies. However, there are cases where not all neighboring spins can be arranged to simultaneously minimize their interaction energies. Magnetic materials exhibiting this behavior are called frustrated magnets. Unlike typical magnets, frustrated magnets exhibit exotic phases and phenomena due to strong quantum fluctuations, such as quantum spin liquids, fractionalized Fermi liquids, and partial Kondo screening effects. These quantum fluctuations become much stronger as the system's dimensionality decreases. Therefore, in this thesis, I studied the emergence of various novel phases in 2D frustrated magnets and their electrical, magnetic, and thermal properties using various numerical approaches. In the kagome lattice with 1/3 filling, I found emergent chiral spin ordering with a Chern insulating phase due to the interplay of Hubbard interaction, spin-orbit coupling, and geometrical frustration using Hartree-Fock and effective model approach. In the Kondo lattice and anti-ferromagnetic \(J_{1}-J_{2}\) model on the honeycomb lattice with 1/4 electron filling, I discovered a partial Kondo-induced fractionalized chiral superconductor with power-law decaying thermal conductivity in the frustrated limit (\(J_{2} > J_{1}\)) using self-consistent mean-field theory and exact diagonalization. Finally, a variational Monte Carlo study of the \(J_{1}-J_{d}-J_{\chi}\) model on the kagome lattice reveals a new class of chiral spin liquids: the ``Dirac chiral spin liquid'' for the intermediate \(J_{\chi}\) regime and the ``staggered chiral spin liquid'' for the sufficiently large \(J_{\chi}\) limit.