Phase diagram of the one-dimensional anisotropic Kondo-necklace model

Abstract

The one-dimensional anisotropic Kondo-necklace model has been studied by several methods. It is shown that a mean field approach fails to gain the correct phase diagram for the Ising-type anisotropy. We then applied the spin wave theory which is justified for the anisotropic case. We have derived the phase diagram between the antiferromagnetic long range order and the Kondo singlet phases. We have found that the exchange interaction ͑J͒ between the itinerant spins and local ones enhances the quantum fluctuations around the classical long range antiferromagnetic order and finally destroy the ordered phase at the critical value J c . Moreover, our results show that the onset of anisotropy in the XY term of the itinerant interactions develops the antiferromagnetic order for J Ͻ J c . This is in agreement with the qualitative feature which we expect from the symmetry of the anisotropic XY interaction. We have justified our results by the numerical Lanczos method where the structure factor at the antiferromagnetic wave vector diverges as the size of system goes to infinity.

Gap formation and phase transition of the anisotropic Kondo necklace model: Density matrix renormalization group analysis

“…The gap and the correlation functions present features similar to what is expected in a Kosterlitz-Thouless transition. Our phase diagram is quantitatively different from that obtained by Mahmoudian and Langari for smaller systems, 18 the former showing a more abrupt tendency for small anisotropies and a slower variation for larger ones. Nevertheless, our diagram supports the idea that there is a quantum phase transition at a finite J for any Ͼ 0.…”

“…IV we show the resulting phase diagram, and compare it to that of Mahmoudian and Langari. 18 The conclusions are presented in Sec. V.…”

“…This parameter takes values from =0 ͑original Kondo necklace͒ to =1 ͑full anisotropic case͒. Different results for the quantum critical behavior of this model ͑in one dimension, at zero temperature͒ have been obtained: using a real-space renormalization group 17 it was determined that for Ͼ 0.58, there was a phase transition at a finite J / t, and that for Ͻ 0.58, the system was in the Kondo singlet phase for all nonzero values of J / t. Using spin wave theory and a numerical Lanczos method for systems up to 24 sites, 18 it was seen that there was always a phase transition for Ͼ 0, and with the bondoperator method, 19 no transition at finite J / t for any anisotropy was found.…”

Thermodynamic quantum critical behavior of the anisotropic Kondo necklace model

“…Thereby, it is always nonzero for any d, supporting its disordered phase, characteristic of 1d Kondo lattices [11,25]. However, it was reported in the production of this report a study for the AKNM in 1d using spin wave approach [26], which gives a critical value d c that separates the disordered Kondo spin liquid state from the AF phase. In our case, using a bond-operator mean field approximation in 1d, we did not find this critical value.…”

Quantum phase transitions in the Kondo-necklace model: perturbative continuous unitary transformation approach

“…Thus the very existence of a quantum phase transition in the one-dimensional model is not justified; this still requires more exhaustive analysis. In contrast, the Z 2 -symmetric Kondo-necklace model shows a quantum phase transition from the Kondo-singlet phase to the antiferromagnetic ordered phase 25 . A particularly interesting result of our formalism is an observation about the n-leg ladder.…”