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Journal of Physics Condensed Matter

Quasi-one-dimensional Heisenberg antiferromagnetic model for an organic polymeric chain

Fang Wu, W Z Wang

Published Mar 30, 2006• 2 citations
Publisher

Abstract

Using the exact diagonalization technique, we study the properties of the ground state of a spin- antiferromagnetic Heisenberg model for a zigzag polymer chain with side radicals connected to the even sites. We consider the nearest-neighbour exchange J and the next-nearest-neighbour exchange ?J along the main chain, and J1 between the even site on the main chain and the radical site. For small ? the ground state is ferrimagnetic. For ?>?c 1, the ground state is a spiral phase, which is characterized by a peak of the static structure factor S(q) locating at an incommensurate value qmax. For ?>?c 2, the ground state is antiferromagnetic. With increasing J1, ?c 1 decreases while ?c 2 has a maximum at about J1 = 0.5. For very small J1 and ? = 0.5, the spin configuration on the main chain is a product of nearest-neighbour singlets. In the antiferromagnetic phase, if J1 is large enough the even site and the radical site form a singlet with exchange-decoupling from the odd site while the odd sites approximately form an antiferromagnetic chain.

DOI
10.1088/0953-8984/18/15/026

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Using the exact diagonalization technique, we study the properties of the ground state of a spin- antiferromagnetic Heisenberg model for a zigzag polymer chain with side radicals connected to the even sites. We consider the nearest-neighbour exchange J and the next-nearest-neighbour exchange ?J along the main chain, and J1 between the even site on the main chain and the radical site. For small ? the ground state is ferrimagnetic. For ?>?c 1, the ground state is a spiral phase, which is characterized by a peak of the static structure factor S(q) locating at an incommensurate value qmax. For ?>?c 2, the ground state is antiferromagnetic. With increasing J1, ?c 1 decreases while ?c 2 has a maximum at about J1 = 0.5. For very small J1 and ? = 0.5, the spin configuration on the main chain is a product of nearest-neighbour singlets. In the antiferromagnetic phase, if J1 is large enough the even site and the radical site form a singlet with exchange-decoupling from the odd site while the odd sites approximately form an antiferromagnetic chain.
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J1FJ_1^FJ1F​) and antiferromagnetic (J1AJ_1^AJ1A​) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (J2FJ_2^FJ2F​). In this model frustration is induced by the non-zero J2FJ_2^FJ2F​ and the effect of dimerization is realized by changing the strength of J1AJ_1^AJ1A​ for a fixed value of J1FJ_1^FJ1F​. The model with site spin sss behaves like a Haldane spin chain with site spin 2sss in the limit of vanishing J2FJ_2^FJ2F​ and large J1F/J1AJ_1^F/J_1^AJ1F​/J1A​. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of J1A−J2FJ_1^A-J_2^FJ1A​−J2F​ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
We use the density matrix renormalization group method to study the ground-state "phase" diagram and some low-energy properties of an antiferromagnetic spin-1 chain with a next-nearest-neighbour exchange J 2 and an alternation δ of the nearest-neighbour exchanges. We find a line running from a gapless point at ( J 2 ,δ) = (0,0.25 ± 0.01) up to a "gapless" point at (0.73 ± 0.005,0) such that the open-chain ground state is fourfold degenerate below the line and is unique above it. A disorder line 2 J 2 + δ = 1 runs from δ = 1 to about δ = 0.136. To the left of this line, the peak in the structure factor S ( q ) is at π, while to the right of the line, it is at less than π.
We use the coupled cluster method for infinite chains complemented by exact diagonalization of finite periodic chains to discuss the influence of a third-neighbor exchange J(3) on the ground state of the spin-½ Heisenberg chain with ferromagnetic nearest-neighbor interaction J(1) and frustrating antiferromagnetic next-nearest-neighbor interaction J(2). A third-neighbor exchange J(3) might be relevant to describe the magnetic properties of the quasi-one-dimensional edge-shared cuprates, such as LiVCuO(4) or LiCu(2)O(2). In particular, we calculate the critical point J(2)(c) as a function of J(3), where the ferromagnetic ground state gives way for a ground state with incommensurate spiral correlations. For antiferromagnetic J(3) the ferro-spiral transition is always continuous and the critical values J(2)(c) of the classical and the quantum model coincide. On the other hand, for ferromagnetic J3 is < or approximately equal to -(0.01...0.02)|J1|. the critical value J(2)(c) of the quantum model is smaller than that of the classical model. Moreover, the transition becomes discontinuous, i.e. the model exhibits a quantum tricritical point. We also calculate the height of the jump of the spiral pitch angle at the discontinuous ferro-spiral transition.
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