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 s=1/2 quantum spin model with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interactions is considered. The behavior of the system in the vicinity of the transition point from the antiferromagnetic ground state to the ferromagnetic one is studied. The consideration is based on the classical approximation and the regular procedure is proposed to find the corrections to the classical energy. The dependence of the energy on spin S is calculated. We obtain evidence of a phase separation for the state with intermediate S. \textcopyright{} 1996 The American Physical Society.
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 .
Quantum corrections of the biquadratic interaction in the 1D spin-1/2 frustrated ferromagnetic Heisenberg model are studied. The biquadratic interaction for spin-1/2 chains is eliminated and transformed to the quadratic interaction. Doing a numerical experiment, new insight as to how the classical phases get modified on the inclusion of quantum fluctuations is provided. Observed results suggest the existence of an intermediate region in the ground state phase diagram of the frustrated ferromagnetic spin-1/2 chains with combination of dimer and chiral orders. In addition, from the quantum entanglement view point, differences between quantum phases are also obtained. The nearest neighbor spins never be entangled in the frustrated ferromagnetic chains but are entangled up to the Majumdar-Ghosh point in the frustrated antiferromagnetic chains. On the other hand, the next nearest neighbor spins in the mentioned intermediate region are entangled.
Abstract We have studied the ground state phases of the one-dimensional (1D) spin-1/2 anisotropic frustrated ferromagnetic model, using the numerical Lanczos method. We have focused on the quantum correlations as the concurrence and the quantum discord (QD) between the nearest neighbor (NN) and the next-nearest neighbor (NNN) spins. Numerical results show that the Tomonaga-Luttinger liquid (TLL), the even-parity dimer, and the vector chiral phases can be distinguished from each other using the long-distance quantum correlations. Specially, the critical points are explicitly detected in the first derivative of the concurrence between the nearest neighbor spins with respect to the frustration parameter.
We study the ground state properties of the Heisenberg spin-
21 chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions using two approximate methods. One of them is the Jordan-Wigner mean-field theory and another approach is based on the transformation of spin operators to Bose ones and on the variational treatment of bosonic Hamiltonian. Both approaches give close results for the ground state energy and the magnetization curve at
T=0. It is proved that quantum fluctuations change the classical critical exponents in the vicinity of the transition point from the ferromagnetic to the singlet ground state. The magnetization processes display a different behavior in the regions near and far from the transition point. The relation of the obtained results to the experimental magnetization curve in
Rb2Cu2Mo3O12 is discussed.