Frustration and multicriticality in the antiferromagnetic spin-1 chain
The antiferromagnetic spin-1 chain has a venerable history and has been thought to be well understood. Here, we show that inclusion of both next-nearest-neighbor (α) and biquadratic (β)interactions results in a rich phase diagram with a multicritical point that has not been observed before. We study the problem using a combination of the density matrix renormalization group (DMRG), an analytic variational matrix product state wave function, and conformal field theory. For negative β<β∗, we establish the existence of a spontaneously dimerized phase, separated from the Haldane phase by the critical line αc(β) of second-order phase transitions. In the opposite regime, β>β∗, the transition from the Haldane phase becomes first order into the next-nearest-neighbor (NNN) AKLT phase. Based on the field theoretical arguments and DMRG calculations, we find that these two regimes are separated by a multicritical point (β∗,α∗) of a different universality class, described by the level-4 SU(2) Wess-Zumino-Witten conformal theory. From the DMRG calculations, we estimate this multicritical point to lie in the range −0.2<β∗<−0.15 and 0.47<α∗<0.53. We further find that the dimerized and NNN-AKLT phases are separated from each other by a line of first-order phase transitions that terminates at the multicritical point. We establish that transitions out of the Haldane phase into the dimer or NNN-AKLT phases are topological in nature and occur either with or without closing of the bulk gap, respectively. We also study short-range incommensurate-to-commensurate transitions in the resulting phase diagram. Inside the Haldane phase, we show the existence of two incommensurate crossovers: the Lifshitz transition and the disorder transition of the first kind, marking incommensurate correlations in momentum and real space, respectively. Notably, these crossover lines stretch across the entire (β,α) phase diagram, merging into a single incommensurate-to-commensurate transition line for negative β≲β∗ inside the dimer phase. This behavior is qualitatively similar to that seen in classical frustrated two-dimensional spin models, by way of the quantum (1+1)D to classical 2D correspondence.
Pixley, J.H., Shashi, Aditya and Nevidomskyy, Andriy H.. "Frustration and multicriticality in the antiferromagnetic spin-1 chain." Physical Review B, 90, no. 21 (2014) American Physical Society: https://doi.org/10.1103/PhysRevB.90.214426.