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Frustration and Multicriticality in the Antiferromagnetic Spin-1 Chain
We study the spin Heisenberg chain, with nearest neighbor, next nearest
neighbor () and biquadratic () interactions using a combination
of the density matrix renormalization group (DMRG), an analytic variational
matrix product state wavefunction, and non-Abelian bosonization. We study the
effect of frustration () on the Haldane phase with
which reveals a rich phase diagram. For , we establish the
existence of a spontaneously dimerized phase for large ,
separated from the Haldane phase by the critical line of
second-order phase transitions connected to the Takhtajan--Babudjian integrable
point . In the opposite regime, , the
transition from the Haldane phase becomes first-order into the next nearest
neighbor (NNN) AKLT phase. Based on field theoretical arguments and DMRG
calculations, we conjecture that these two regimes are separated by a
multicritical point () of a different universality
class, described by the Wess--Zumino--Witten critical theory. From
the DMRG calculations we estimate this multicritical point to lie in the range
and . We find that the
dimerized and NNN-AKLT phases are separated by a line of first-order phase
transitions that terminates at the multicritical point. 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. We show
these crossover lines stretch across the entire phase diagram,
merging into a single incommensurate-to-commensurate transition line for
negative outside the Haldane phase.Comment: 25 pages, 24 figures, updated with published versio
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