Dimerization and effective decoupling in two spin-1 generalizations of the spin-1/2 Majumdar-Ghosh chain

Natalia Chepiga; Frédéric Mila

doi:10.1103/PhysRevB.100.104426

paper

Dimerization and effective decoupling in two spin-1 generalizations of the spin-1/2 Majumdar-Ghosh chain

arXiv:1907.11472 · doi:10.1103/PhysRevB.100.104426

Abstract

We perform a systematic DMRG investigation of the two natural spin-1 generalizations of the spin-1/2 Majumdar-Ghosh chain, the spin-1 $J_{1} - J_{2}$ Heisenberg chain, where $J_{2}$ is a next-nearest neighbor Heisenberg coupling, and the spin-1 $J_{1} - J_{3}$ model, where $J_{3}$ refers to a three-site interaction defined by $J_{3} [(S_{i - 1} \cdot S_{i}) (S_{i} \cdot S_{i + 1}) + H.c.]$ . Although both models are rigorously equivalent to the Majumdar-Ghosh chain for spin-1/2, their physics appears to be quite different for spin 1. Indeed, when all couplings are antiferromagnetic, the spin-1 $J_{1} - J_{2}$ model undergoes an effective decoupling into two next-nearest neighbour (NNN) Haldane chains upon increasing $J_{2}$ , while the $J_{1} - J_{3}$ chain undergoes a spontaneous dimerization similar to the spin-1/2 Majumdar-Ghosh chain upon increasing $J_{3}$ . By extending the phase diagram to all signs of the couplings, we show that both the dimerized and the NNN-Haldane phase are actually present in the $J_{1} - J_{3}$ model, the former one adjacent to the Haldane one, the latter one to the ferromagneric one, with an Ising transition between them. By contrast, the $J_{1} - J_{2}$ chain only has a NNN-Haldane phase between the Haldane phase and the ferromagnetic phase for positive $J_{2}$ . In both cases, our DMRG data are consistent with a continuous Kosterlitz-Thouless transition between the NNN-Haldane and the ferromagnetic phases.

arXiv comment13 pages, 15 figures

Dimerization and effective decoupling in two spin-1 generalizations of the spin-1/2 Majumdar-Ghosh chain

Abstract

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