Journal of Statistical Physics

, Volume 79, Issue 1–2, pp 347–376 | Cite as

Ground-state energy of a quantum chain with competing interactions

  • C. E. I. Carneiro
  • M. J. de Oliveira
  • W. F. Wreszinski


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.

Key Words

Quantum chain competing interactions ferromagnetic and helical ground state spin waves variational wave functions 


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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • C. E. I. Carneiro
    • 1
  • M. J. de Oliveira
    • 1
  • W. F. Wreszinski
    • 1
  1. 1.Instituto de FísicaUniversidade de São PauloSão PauloBrazil

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