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arXiv:cond-mat/0303201 · Physical review. B, Condensed matter

Random antiferromagnetic spin- 12 chains with competing interactions

Eddy Yusuf, Kun Yang

Published Jul 30, 2003• 18 citations
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Abstract

We study disordered antiferromagnetic spin-$\frac{1}{2}$ chains with nearest- and further-neighbor interactions using the real-space renormalization-group method. We find that the system supports two different phases, depending on the ratio of the strength between nearest-neighbor and further-neighbor interactions as well the bond randomness strength. For weak further-neighbor coupling the system is in the familiar random singlet phase, while stronger further-neighbor coupling drives the system to a large spin phase similar to that found in the study of random antiferromagnetic-ferromagnetic spin chains. The appearance of the large spin phase in the absence of ferromagnetic coupling is due to the frustration introduced by further-neighboring couplings, and is unique to the disordered chains.

DOI
10.1103/physrevb.68.024425

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We study the magnetic properties of two types of one-dimensional XXXXXX spin-12\frac{1}{2}21​ chains. The first type has only nearest-neighbor interactions which can be either antiferromagnetic or ferromagnetic, and the second type has both nearest-neighbor and next-nearest-neighbor interactions, but only antiferromagnetic in character. We study these systems in the presence of low magnetic fields both analytically and numerically. Comparison of results shows a close relation between the two systems, which is in agreement with results previously found in Heisenberg chains by means of a numerical real-space renormalization-group procedure.
We study the spin-1 chain with nearest neighbor couplings that are rotationally invariant, but include both Heisenberg and biquadratic exchange, with random strengths. We demonstrate, using perturbative renormalization group methods as well as exact diagonalization of clusters, that the system generates ferromagnetic couplings under certain circumstances even when all the bare couplings are antiferromagnetic. This disorder induced instability leads to formation of large magnetic moments at low temperatures, and is a purely quantum mechanical effect that does not have a classical counterpart. The physical origin of this instability, as well as its consequences, are discussed.
We study frustrated ferromagnetic spin-1 chains, where the ferromagnetic nearest-neighbor coupling competes with the antiferromagnetic next-nearest-neighbor coupling. We use the density-matrix renormalization group to obtain the ground states. Through the analysis of spin-spin correlations we identify the double Haldane phase as well as the ferromagnetic phase. It is shown that the ferromagnetic coupling leads to incommensurate correlations in the double Haldane phase. Such short-range correlations transform continuously into the ferromagnetic instability at the transition to the ferromagnetic phase. We also compare the results with the spin-1/2 and classical spin systems and discuss the string orders in the system.
The low energy properties of the spin-1/2 random Heisenberg chain with ferromagnetic and antiferromagnetic interactions are studied by means of the density matrix renormalization group (DMRG) and real space renormalization group (RSRG) method for finite chains. The results of the two methods are consistent with each other. The deviation of the gap distribution from that of the random singlet phase and the formation of the large-spin state is observed even for relatively small systems. For a small fraction of the ferromagnetic bond, the effect of the crossover to the random singlet phase on the low temperature susceptibility and specific heat is discussed. The crossover concentration of the ferromagnetic bond is estimated from the numerical data.
A random antiferromagnetic spin-1 chain with both Heisenberg and biquadratic nearest neighbor couplings is found to exhibit a novel ferromagnetic-like instability at low energies, if there is competition between the Heisenberg and biquadratic couplings, even though each individual nearest neighbor coupling is such as to produce a singlet ground state for the isolated pair. This instability leads to the generation of ferromagnetic couplings, and thus to the formation of weakly coupled large moments at low temperatures. A perturbative calculation (up to 4th order) is performed to investigate whether such a situation is physically realizable in spin-1 systems.