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arXiv:0710.3239 · Physical Review B

Phase diagram of the one-dimensional S=12 XXZ model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions

Rouhollah Jafari, A. Langari

Published Jul 10, 2007• 64 citations
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Abstract

We have studied the phase diagram of the one-dimensional $S=\frac{1}{2}$ $XXZ$ model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. We have applied the quantum renormalization group (QRG) approach to obtain stable fixed points and the scaling of coupling constants. The QRG prescription has to be implemented to the second order of interblock interactions to obtain a self-similar Hamiltonian after each step of the QRG. This model shows a rich phase diagram which includes quantum spin-fluid and dimer phases in addition to the classical N\'eel and ferromagnetic ones. We have found the border between different phases by tracing the scaling of coupling constants.

DOI
10.1103/physrevb.76.014412

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The one dimensional S=1 XXZ model with next-nearest-neighbor interaction ααα and Ising-type anisotropy ΔΔΔ is studied by using a numerical diagonalization technique. We discuss the ground state phase diagram of this model numerically by the twisted-boundary-condition level spectroscopy method and the phenomenological renormalization group method, and analytically by the spin wave theory. We determine the phase boundaries among the XY phase, the Haldane phase, the ferromagnetic phase and the Néel phase, and then we confirm the universality class. Moreover, we map this model onto the non-linear σσσ model and analyze the phase diagram in the ααα ≪\ll≪ -1 and ΔΔΔ ∼\sim∼ 1 region by using the renormalization group method.
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