Speaker
Description
Frustrated magnets provide fertile ground for unconventional orders and emergent excitations. In particular, chiral states break time-reversal symmetry and host emergent gauge fluxes that can endow quasiparticles with nontrivial topology~[1,2,3]. Here, we explore two complementary aspects: topological magnon transport and exactly solvable spin models.
On the triangular lattice, we study a spin-1/2 isotropic Heisenberg model with further-neighbor exchanges and ring exchange. The four-site ring exchange stabilizes a chiral four-sublattice noncoplanar order, which generates finite Berry curvature in the magnon bands and produces a thermal Hall effect even without Dzyaloshinskii-Moriya interactions. Using variational methods, we further show that this ordered phase can melt into a chiral spin liquid, continuously connected to the $U(1)$ Dirac spin liquid in the absence of ring exchange.
On corner-sharing tetrahedral lattices, we construct local frustration-free parent Hamiltonians whose exact ground-state manifolds contain chiral four-coloring spin configurations. These states generalize ice-rule constraints to a finite set of noncoplanar spin directions and possess intrinsic scalar chirality. For arbitrary spin-S, including the classical limit, the local Hamiltonian can be written as a positive-semidefinite form. Using a Schwinger-boson formulation, we identify the structure of the zero-energy manifold and show that it contains an extensive degeneracy on checkerboard and pyrochlore lattices. Our construction provides a systematic route to stabilizing chiral phases in frustrated quantum magnets.