Characterizing ground states of low-dimensional quantum magnets

Clebson Cruz

Adam Iaizzi

Cristian D. Batista, S. A. Trugman

We introduce a frustrated spin 1/2 Hamiltonian which is an extension of the two dimensional J1-J2 Heisenberg model. The ground states of this model are exactly obtained at a first-order quantum phase transition between two valence bond crystals. At this point, the low energy excitations are deconfined spinons and spin-charge separation occurs under doping in the limit of low concentration of holes. In addition, this point is characterized by the proliferation of topological defects.

Gang Su

Haiping Hu, Huaiming Guo, Shu Chen

We report the findings of fractional topological states in one-dimensional periodically modulated quantum spin chains with up to third neighbor interactions. By exact numerical studies, we demonstrate the existence of topologically nontrivial degenerate ground states at some specific magnetizations, which can be characterized by the nonzero-integer total Chern numbers of the degenerate ground states and the emergence of nontrivial edge states under open boundary conditions. We find that the low-energy excitations obey bosonic $\ensuremath{\nu}=1/2$ fractional statistics for the spin-$1/2$ system and $\ensuremath{\nu}=1$ non-Abelian statistics for the spin-1 system, respectively. The discovered fractional quantum states provide another route to the theoretical exploration of fractional quantum states in correlated spin systems.

Kirill Yu. Povarov