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arXiv:cond-mat/0205492 · Physical Review Letters

Phase Diagram of the Random Heisenberg Antiferromagnetic Spin-1 Chain

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

Published Aug 22, 2002• 36 citations
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Abstract

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.

DOI
10.1103/physrevlett.89.117202

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We introduce variants of the Ma-Dasgupta renormalization-group (RG) approach for random quantum spin chains, in which the energy-scale is reduced by decimation built on either perturbative or non-perturbative principles. In one non-perturbative version of the method, we require the exact invariance of the lowest gaps, while in a second class of perturbative Ma-Dasgupta techniques, different decimation rules are utilized. For the S = 1 random antiferromagnetic Heisenberg chain, both type of methods provide the same type of disorder dependent phase diagram, which is in agreement with density-matrix renormalization-group calculations and previous studies.
We investigate the application of a perturbative renormalization group (RG) method to random antiferromagnetic Heisenberg chains with arbitrary spin size. At zero temperature we observe that initial arbitrary probability distributions develop a singularity at J=0,J=0,J=0, for all values of spin S. When the RG method is extended to finite temperatures, without any additional assumptions, we find anomalous results for S> 1.S>~1.S> 1. These results lead us to conclude that the perturbative scheme is not adequate to study random chains with S> 1.S>~1.S> 1. Therefore a random singlet phase in its more restrictive definition is only assured for spin-1/2 chains.
Combining quantum Monte Carlo simulations with the maximum entropy method, we study the dynamical structure factor S(k,ω)S(k,ω)S(k,ω) of spin-1/2 antiferromagnetic Heisenberg chains with various random bond distributions. We emphasize the crossover behavior in the dynamical properties from pure chain to disorder-dominated random singlet phase due to bond randomness. For the distribution corresponding to the infinite randomness fixed point, S(k,ω)S(k,ω)S(k,ω) develops broad non-spinon excitations as well as the random-singlet peak near (k,ω)=(π,0)(k, ω) = (π, 0)(k,ω)=(π,0), consistent with the known results obtained by the real-space renormalization group method. For weak disorder, however, we find clear signature of spinon excitations, reminiscent of pure spin chains, blurred by disorder. We discuss the implication for experiments on random-bond antiferromagnetic spin chains, realizable, e.g., in BaCu2_22​(Six_xx​Ge1−x_{1-x}1−x​)2_22​O7_77​.
We use extensive density matrix renormalization group (DMRG) calculations to explore the phase diagram of the random S=1S=1S=1 antiferromagnetic Heisenberg chain with a power-law distribution of the exchange couplings. We use open chains and monitor the lowest gaps, the end-to-end correlation function and the string order parameter. For this distribution at weak disorder, the system is in the gapless Haldane phase with a disorder dependent dynamical exponent, zzz, and z=1z=1z=1 signals the border between the nonsingular and singular regions of the local susceptibility. For strong enough disorder, which approximately corresponds to a uniform distribution, a transition into the random singlet phase is detected, at which the string order parameter as well as the average end-to-end correlation function are vanishing and at the same time the dynamical exponent is divergent. Singularities of physical quantities are found to be somewhat different in the random singlet phase and in the critical point.
We use a modified perturbative renormalization group approach to study the random quantum antiferromagnetic spin-32\frac{3}{2}23​ chain. We find that in the case of rectangular distributions there is a quantum Griffiths phase, and we obtain the dynamical critical exponent Z as a function of disorder. Only in the case of extreme disorder, characterized by a power-law distribution of exchange couplings, we find evidence that a random singlet phase could be reached. We discuss the differences between our results and those obtained by other approaches.