We study one-dimensional lattice anyons with extended Hubbard interactions at unit filling using bosonization and numerical simulations. The behavior can be continuously tuned from bosonic to fermionic statistics by adjusting the topological exchange angle θ, which leads to a competition of different instabilities. We present the bosonization theory in the presence of dynamic gauge fields, which predicts a phase diagram of four different gapped phases with distinct dominant correlations. Advanced numerical simulations determine and analyze the exact phase transitions between Mott insulator, charge density wave, dimerized state, and Haldane insulator, all of which meet at a multicritical line in the parameter space of anyonic angle θ, on-site interaction U, and nearest neighbor repulsion V. Superfluid and pair-superfluid phases are stable in a region of small V.
We systematically study the effects of higher-order interactions on the
S=23,1 orthogonal dimer chains using exact diagonalization and density matrix renormalization group. Due to frustration and higher spin, there are rich quantum phases, including three Haldane phases, two gapless phases, and several magnetically ordered phases. To characterize these phases and their phase transitions, we study various physical quantities such as energy gap, energy-level crossing, fidelity susceptibility, spin correlation, entanglement spectrum, and central charge. According to our calculations, the biquadratic term can enhance the Haldane phase regions. In particular, we numerically identify that a Haldane phase in
S=23 case is adiabatically connected to the exact AKLT (Affleck, Kennedy, Lieb, and Tasaki) point when adding a bicubic term. Our study on the orthogonal dimer model, which is a 1D version of the Shastry-Sutherland model, provides insights into understanding the possible
S=23,1 Haldane phases in quasi-1D and 2D frustrated magnetic materials.
Department of Physics, Shahre-Ray branch, Islamic Azad University, Tehran, Iran.(Dated: April 16, 2012)We have considered the 1D dimerized frustrated antiferromagnetic (ferromagnetic) Heisenbergmodel with arbitrary spin S. The exact classical magnetic phase diagram at zero temperature isdetermined using the LK cluster method. Cluster method results, show that the classical groundstate phase diagram of the model is very rich including first and second-order phase transitions. Inthe absence of the dimerization, a second-order phase transition occurs between antiferromagnetic(ferromagnetic) and spiral phases at the critical frustration α