Abstract
We show rigorously that the ground state of a quantum chain with competing ferromagnetic nearest and antiferromagnetic next nearest interactions undergoes a transition from ferromagnetic to helical type, in the isotropic case, for a certain value of the relevant ratio of coupling constants. Boundaries of the phase diagram are also determined in the anisotropic case. The stability of a special quantum state (corresponding to a classical modulated phase of ⫇=п/3) is analyzed by an extension of Holstein-Primakoff arguments, along a line of constant ratio of couplings, showing in particular a sequence of (instability) gaps. Finally, a natural adaptation of a variational wave function due to Huse and Elser is used to study several portions of the phase diagram, with very good agreement with previous theoretical results.
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Carneiro, C.E.I., de Oliveira, M.J. & Wreszinski, W.F. Ground-state energy of a quantum chain with competing interactions. J Stat Phys 79, 347–376 (1995). https://doi.org/10.1007/BF02179393
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DOI: https://doi.org/10.1007/BF02179393