Topological phases with broken time-reversal symmetry and Chern number |C|>=2 are of fundamental interest, but it remains unclear how to engineer the desired topological Hamiltonian within paradigm spin-orbit-coupled particles hopping only between nearest neighbours a static lattice. We show that higher arise when spin-orbit coupling satisfies combination spin spatial rotation symmetries. lever...

In this paper, we present some inequalities for the Co-PI index involving the some topological indices, the number of vertices and edges, and the maximum degree. After that, we give a result for trees. In addition, we give some inequalities for the largest eigenvalue of the Co-PI matrix of G.

We study the general structure of Smirnov's axioms on form factors of local operators in integrable models. We find various consistency conditions that the form factor functions have to satisfy. For the special case of the O(3) σ-model we construct simple polynomial solutions for the operators of the spin-field, current, energy-momentum tensor and topological charge density.