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

Abstract

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 SO(N=3, 4, 5) BLBQ chains by a world-line Monte-Carlo simulation for the N-color bosonic particle model.

published in PRB

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• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets
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• Spin nematics, valence-bond solids and spin liquids in SO($N$) quantum spin models on the triangular lattice
• Efficient Quantum Monte Carlo simulations of highly frustrated magnets: the frustrated spin-1/2 ladder
• Mitigating the Sign Problem Through Basis Rotations
• Duality, Criticality, Anomaly, and Topology in Quantum Spin-1 Chains
• Resolution of the Sign Problem for a Frustrated Triplet of Spins
• Reduction of the sign problem near $T=0$ in quantum Monte Carlo simulations
• Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains
• Lowest-energy states in parity-transformation eigenspaces of SO(N) spin chain
• Lowest energy states of an $O(N)$ fermionic chain
• Identification of gapless phases by a twisting operator
• Angular-time evolution for the Affleck-Kennedy-Lieb-Tasaki chain and its edge-state dynamics