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.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.

arXiv:cond-mat/0205492Physical Review LettersAug 22, 200236 citations

Thermodynamics of the random antiferromagnetic spin-1 chain

A. Saguia, B. Boechat, M. A. Contínentino

Journal of Magnetism and Magnetic MaterialsMay 1, 20011 citation

Random Antiferromagnetic Spin-1 Chains

R. A. Hyman, Steve Girvin, Kun Yang +1 more

APSMar 1, 19962 citations

Phase diagrams and universality classes of random antiferromagnetic spin ladders

José A. Hoyos, E. Miranda

The random antiferromagnetic two-leg and zigzag spin- $1∕2$ ladders are investigated using the real space renormalization group scheme and their complete phase diagrams are determined. We demonstrate that the first system belongs to the same universality class of the dimerized random spin- $1∕2$ chain. The zigzag ladder, on the other hand, is in a random singlet phase at weak frustration and disorder. Otherwise, we give additional evidence that it belongs to the universality class of the random antiferromagnetic and ferromagnetic quantum spin chains, although the universal fixed point found in the latter system is never realized. We find, however, a new universal fixed point at intermediate disorder.The random antiferromagnetic two-leg and zigzag spin-$1∕2$ ladders are investigated using the real space renormalization group scheme and their complete phase diagrams are determined. We demonstrate that the first system belongs to the same universality class of the dimerized random spin-$1∕2$ chain. The zigzag ladder, on the other hand, is in a random singlet phase at weak frustration and disorder. Otherwise, we give additional evidence that it belongs to the universality class of the random antiferromagnetic and ferromagnetic quantum spin chains, although the universal fixed point found in the latter system is never realized. We find, however, a new universal fixed point at intermediate disorder.

arXiv:cond-mat/0404444Physical Review BJun 9, 200423 citations

The random antiferromagnetic two-leg and zigzag spin-

1∕2

ladders are investigated using the real space renormalization group scheme and their complete phase diagrams are determined. We demonstrate that the first system belongs to the same universality class of the dimerized random spin-

1∕2

chain. The zigzag ladder, on the other hand, is in a random singlet phase at weak frustration and disorder. Otherwise, we give additional evidence that it belongs to the universality class of the random antiferromagnetic and ferromagnetic quantum spin chains, although the universal fixed point found in the latter system is never realized. We find, however, a new universal fixed point at intermediate disorder.