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Physical review. B, Condensed matter

Antiferromagnet-ferromagnet transition in the one-dimensional frustrated spin model

V. Ya. Krivnov, А. А. Овчинников

Published Mar 1, 1996• 30 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.53.6435

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•Jan 1, 2012•0 citations
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 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 −8γ2-8γ^2−8γ2.
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 stability of the ferromagnetic phase of the two-dimensional (2D) quantum spin-1/2 model with nearest-neighbor ferro- and next-nearest neighbor antiferromagnetic interactions is studied. It turns out that values of exchange integrals at which the ferromagnetic state becomes unstable with respect to a creation of one and two magnons are different. This difference shows that the classical approximation is inapplicable to the study of the transition from the ferromagnetic to the singlet state in contrast with 1D case. This problem is investigated using a variational function. It is based on the boson representation of spin operators which is different from the Holstein-Primakoff approximation. This allows us to obtain an accurate estimate of the transition point and to study the character of the phase transition.
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.
By using the density matrix renormalization group(DMRG) method,the author investigates the diagram of the one-dimensional frustrated anisotropic ferromagnetic S=1 Heisenberg spin model,in which the nearest neighboring interactions are anisotropic ferromagnetic and the next nearest neighboring exchanges are considerable anti-ferromagnetic.The ground state energy and both the in-plane and out-of-plane spin correlation functions are calculated.Apart from the ferromagnetic phase and the spin-fluid phase in the small frustration region,but in the large frustration region,it is identified that spin correlations decay with a short-range exponential law and an oscillating behavior.The result is different from the previous result for S=1/2.
In this work the ordering processes in classical frustrated Ising models and the ground-state behavior of frustrated quantum spin models are investigated. In the first part the phase transition from a high-temperature paramagnetic phase to a antiferromagnetic ground state is analyzed for the square-lattice Ising model with competing antiferromagnetic interactions between nearest- and next-nearest-neighbor spins. In the case of spatially isotropic interactions the phase transition to a collinear state is of special interest. Using Monte-Carlo simulations on finite lattices as well as field-theoretical methods for the continuous model it is shown that depending on the frustration three different sectors can be distinguished that show (i) Ising-universal behavior (ii) Ashkin-Teller-like non-universal behavior (varying critical exponents) and (iii) non-critical first-order behavior. For spatially anisotropic interactions the emergence of an intermediate incommensurate phase is verified by means of Monte-Carlo simulations which has been predicted by earlier mean-field calculations. The nature of this phase is studied analyzing spin-spin correlation functions and its ordering wave-vector reveals a strong temperature and size dependence. In the second part the influence of quantum fluctuations on classical antiferromagnetic ground states are investigated in anisotropic quantum spin-1/2 Heisenberg models with competing interactions. Using quantum Monte-Carlo simulations, exact diagonalization and perturbation theory the ground-state phase diagrams are calculated for a square lattice with nearest- and next-nearest-neighbor interactions and a honeycomb lattice with up to third-nearest-neighbor interactions whereby the fluctuations are chosen to be non-frustrating. For both cases the stability regions of classical magnetic states are identified and an intermediate phase is detected that shows no sign of long-range magnetic order. Further calculations also rule out valence-bond-crystal or topological order for this state, thus a quantum disordered ground state is stabilized in these models.