Non-existence of long-range-order for a certain 1D model and the soliton picture

Yukiyasu Ozeki, Hidetoshi Nishimori, Yasuhiro Tomita

The existence of long-range order is proved under certain conditions for the antiferromagnetic XYZ model on the simple cubic or the square lattice. In particular, the spin-1/2 XXZ model on the square lattice is shown to have ground-state long-range order if the exchange anisotropy Δ satisfies 0≦ Δ <0.20 or Δ >1.72, which improves the result of Kubo and Kishi. The existence of long-range order of the z -component of the spin operator is proved for the XXZ model with XY -like anisotropy (0≦ Δ ≦1) under certain conditions. A similar result is shown to hold for the long-range order in the x -direction for the Ising-like model ( Δ ≧1). The XXZ model on the two-dimensional hexagonal lattice is proved to have finite ground-state long-range order for any value of Δ (≧0) if S ≧1 and for Δ >2.55 when S =1/2.

Francesco Guerra

F. W. O. da Silva, Antonio S. T. Pires

Zhongbo Yan, Liang Chen, Shaolong Wan

One-dimensional spinless Fermi gas with attractive dipole-dipole interaction is investigated. Results obtained show when the interaction is weak, the excitation spectrum is linear and the superconducting correlation function decays as power law, indicating the validity of the Tomonaga-Luttinger (TL) liquid picture. However, when the interaction reaches a critical value, the excitation spectrum is nonlinear and the superconducting correlation function keeps finite for infinity separation, indicating real long-range order established and the breakdown of the TL liquid picture. We prove that the existence of long-range order is not in contradiction with the Hohenberg theorem and show that this system is related to the Kitaev toy model, therefore, it has potential applications for the future topological quantum computation.

Banasri Basu, P. Bandyopadhyay

Hanbin Pang, Shoudan Liang, James F. Annett

Competition between Mott and Anderson metal-insulator transitions is studied in a one dimensional spinless fermion system of 200 sites. Although the long range charge density wave (CDW) order and gap of the Mott phase are destroyed by weak randomness, the elementary excitations are still solitons based on the local CDW order. The solitons are easily localized in the random potential. Thus for weak randomness and large interaction, a disordered Mott phase exists in which the localization is determined by the local CDW order in contrast to the conventional Anderson localization picture in the weak interaction limit.