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arXiv:cond-mat/9712172 · Physical review. B, Condensed matter

Phases of random antiferromagnetic spin-1 chains

Cécile Monthus, O. Golinelli, Th. Jolicœur

Published Jul 1, 1998• 51 citations
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Abstract

We formulate a real-space renormalization scheme that allows a study of the effects of bond randomness in the Heisenberg antiferromagnetic spin-1 chain. There are four types of bonds that appear during the renormalization flow. We implement the decimation procedure numerically. We give a detailed study of the probability distributions of all these bonds in the phases that occur when the strength of the disorder is varied. Approximate flow equations are obtained in the weak-disorder regime as well as in the strong-disorder case, where the physics is that of the random-singlet phase.

DOI
10.1103/physrevb.58.805

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We formulate a real-space renormalization scheme that allows a study of the effects of bond randomness in the Heisenberg antiferromagnetic spin-1 chain. There are four types of bonds that appear during the renormalization flow. We implement the decimation procedure numerically. We give a detailed study of the probability distributions of all these bonds in the phases that occur when the strength of the disorder is varied. Approximate flow equations are obtained in the weak-disorder regime as well as in the strong-disorder case, where the physics is that of the random-singlet phase.
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We study disordered antiferromagnetic spin-12\frac{1}{2}21​ 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.
The zero-temperature phase diagram of the anisotropic, strongly disordered antiferromagnetic quantum spin-1 chain is investigated, within the framework of a real-space renormalization-group approach. In the presence of uniform anisotropy there occurs a phase transition from a random singlet phase to an Ising antiferromagnetic phase controlled by a fixed point that does not have Heisenberg symmetry. We find evidence of a fixed point due to randomness in the anisotropy similar to that which occurs for quantum Heisenberg spin-12\frac{1}{2}21​ chains.
We present a new perturbative real space renormalization group (RG) to study random quantum spin chains and other one-dimensional disordered quantum systems. The method overcomes problems of the original approach which fails for quantum random chains with spins larger than S=1/2. Since it works even for weak disorder, we are able to obtain the zero temperature phase diagram of the random antiferromagnetic Heisenberg spin-1 chain as a function of disorder. We find a random singlet phase for strong disorder. As the disorder decreases, the system shows a crossover from a Griffiths to a disordered Haldane phase.
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We study the random antiferromagnetic spin-1 chain following the evolution of the bond probability distributions under a renormalization group transformation. We use a mapping of the spin-1 chain into an effective spin-1/2 chain with both ferromagnetic (odd bonds) and antiferromagnetic (even and odd bonds) interactions. We obtain a recursion relation for the coupling constants, solving exactly up to a four-spin cluster. Our improved perturbation treatment on these larger clusters shows that the random singlet phase in the spin-1 chain, differently from previous results, is obtained only when 100100%100 of the odd bonds are strong ferromagnetic, i.e., larger than the even antiferromagnetic bonds. Otherwise the ground state is that of a dimerized spin-1/2 chain.