XXZ-like phase in the F-AF anisotropic Heisenberg chain

Abstract

Abstract. By means of the Density Matrix Renormalization Group technique, we have studied the region where XXZ-like behavior is most likely to emerge within the phase diagram of the F-AF anisotropic extended (J − J ) Heisenberg chain. We have analyzed, in great detail, the equal-time two-spin correlation functions, both in-and out-of-plane, as functions of the distance (and momentum). Then, we have extracted, through an accurate fitting procedure, the exponents of the asymptotic power-law decay of the spatial correlations. We have used the exact solution of XXZ model (J = 0) to benchmark our results, which clearly show the expected agreement. A critical value of J has been found where the relevant power-law decay exponent is independent of the in-plane nearest-neighbor coupling.

Phase diagram of an anisotropic frustrated ferromagnetic spin-12chain in a magnetic field: A density matrix renormalization group study

“…In the isotropic model at small ͉␤͉ the spin gap is predicted to be either zero 21,22 or astronomically small. 23 The zero-field phase diagram of the frustrated ferromagnetic chain with an anisotropic exchange has been studied, both for the case of anisotropic nearest-neighbor interactions only 24,25 and for the case in which both exchange paths exhibit the same anisotropy. [26][27][28][29] For the latter example, relevant to our work, the existence of dimer, spin-fluid, and ͑anti͒ferromagnetically ordered phases has been suggested.…”

Modified equation of motion approach for metallic ferromagnetic systems with the correlated hopping interaction

“…One can conclude that this result is related to differentiating with respect to t and t 0 in the equation of motion method. The composite operator method [18,19], in which we also have the differentiation with respect to t and t 0 , gives the Abrikosov-Suhl resonance peak for particle-hole symmetric case too. In this method one takes into account the higher order Green's functions and consequently one obtains the Abrikosov-Suhl resonance peak, which is narrower than in our method.…”

“…(IPT) [10,11], the equation-of-motion approach [12][13][14][15][16][17] and composite operator method [18][19][20][21]. Each of these methods of solving the SIAM problem has its own limitations.…”

“…The dependence of both time variables t and t 0 is also used in the composite operator method [18][19][20][21]. In this method three composite operators were used.…”

“…These operators describe well the lower and the upper Hubbard subbands and additionally they allow to define the higherorder composite field which describes low-energy dynamics. Applying this method to SIAM made it possible to obtain the Abrikosov-Suhl resonance peak both for symmetric case and for the asymmetric case [18,19].…”