Duality at Lattice Scale around the Takhtajan-Babujain Point in the Bilinear Biquadratic Spin-1 Chain

الأصل · EN

In the literature, it is known that near the Takhtajan-Babujain point of the bilinear-biquadratic spin-1 chain, the low energy theory is captured by three Majorana fermions with a mass sign change, or three Ising chains near the transition. In this paper, we study how the spin-1, the Ising spins, and the fermions are related at lattice scale. We construct the spin-1 operator out from the Ising spins and fermions, showing that when the Ising chains are in the ordered phase, the spin-1 chain is in the dimer phase, and when the Ising chains are in the paramagnetic phase, the spin-1 chain is in the Haldane phase. Through this mapping we can see how unit cell doubling in the dimer phase and the boundary spin-12 zero mode in the Haldane phase take place, even though in the Ising transition neither phenomena exist.