2015/12/03 by Chen, Kuang-Ting · 1 citation
#FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.1512.00967
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-\frac12 zero mode in the Haldane phase take place, even though in the Ising transition neither phenomena exist.