Symmetry-protected topological order and negative-sign problem for SO(N) bilinear-biquadratic chains

Using a generalized Jordan-Wigner transformation combined with the defining representation of the SO(N) spin, we map the SO(N) bilinear-biquadratic(BLBQ) spin chain into the N-color bosonic particle model. We find that, when the Jordan-Wigner transformation disentangles the symmetry-protected topological entanglement, this bosonic model becomes negative-sign free in the context of quantum Monte-Carlo simulation. For the SO(3) case, moreover, the Kennedy-Tasaki transformation for the S=1 BLBQ chain, which is also a topological disentangler, derives the same bosonic model through the dimer-R bases. We present the temperature dependence of the energy, entropy and string order parameter for the SON=3, 4, 5 BLBQ chains by a world-line Monte-Carlo simulation for the N-color bosonic particle model.