An effective approach,the two time Green function method,is applied to analytically investigate the critical value αc of the fluid-dimer transition for the S=1/2 frustrated antiferromagnetic Heisenberg chain,where the nearest neighbor and next neighbor interactions are considered.By using a simple decoupling scheme,the random phase approximation(RPA),it is shown that the analytical result αc=0.242 is in good agreement with the other theoretical estimates.
We present a quantum version of the twist method which has been developed for classical systems. A finite size scaling form for the excess ground state energy is derived and tested for an S =1/2 antiferromagnetic Heisenberg chain with next nearest neighbor interactions: H = J ∑( S j · S j +1 + α S j · S j +2 ) with J >0 and α>0. Using an exact diagonalization method, we obtain the critical value
αc≅0.246 of the fluid-dimer transition, which is very close to the reliable value recently obtained by Okamoto and Nomura (Phys. Lett. A 169 (1992) 433).
We study the quantum spin-
21 Heisenberg model in two dimensions, interacting through a nearest-neighbor antiferromagnetic exchange
(J) and a ferromagnetic dipolarlike interaction
(Jd), using double-time Green's function, decoupled within the random phase approximation. We obtain the dependence of
kBTc∕Jd as a function of frustration parameter $\ensuremath{\delta}$, where
Tc is the ferromagnetic (F) transition temperature and $\ensuremath{\delta}$ is the ratio between the strengths of the exchange and dipolar interaction (i.e., $\ensuremath{\delta}=J∕{J}_{d}$). The transition temperature between the F and paramagnetic phases decreases with $\ensuremath{\delta}$, as expected, but goes to zero at a finite value of this parameter, namely, $\ensuremath{\delta}={\ensuremath{\delta}}_{c}=\ensuremath{\pi}∕8$. At
T=0 (quantum phase transition), we analyze the critical parameter ${\ensuremath{\delta}}_{c}(p)$ for the general case of an exchange interaction in the form
Jij=Jd∕rijp, where ferromagnetic and antiferromagnetic phases are present.
The one-dimensional quantum spin-1/2 model with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interaction is considered. The Hamiltonian is firstly rewritten in a form with rotated spin operators, then bosonized by using the linear spin wave approximation and then treated by using the Green function approach. An integral expression of the quantum correction to the classical ground state energy is derived. The critical behavior of the ground state energy in the vicinity of the transition point from the ferromagnetic to the singlet ground state is analyzed by numerical calculation and the result is −8γ 2 .
The one-dimensional quantum spin-1/2 model with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interaction is considered. The Hamiltonian is first bosonized by using the linear spin wave approximation, and then is treated by using the Green's function approach. An integral expression of the quantum correction to the classical ground state energy is derived. The critical behavior of the ground state energy in the vicinity of the transition point from the ferromagnetic to the singlet ground state is analyzed by numerical calculation, and the result is
−8γ2.
We study the ground-state properties of the one-dimensional anisotropic spin-1/2 antiferromagnetic Heisenberg model with competing antiferromagnetic second-neighbor Ising interaction. Using the modified Lanczos method, we obtain the phase diagram in parameter space and different correlation functions, which we use to characterize the different phases. For small next-nearest-neighbor parameters we evaluate the critical exponent \ensuremath{\eta} of the spin-spin correlation function. We find good agreement between the numerical results and those obtained using the Luther and Peschel approach.