Comment on ``Density Matrix Renormalization Group Study of the Haldane Phase in Random One-Dimensional Antiferromagnets"

In a recent Letter (PRL 83, 3297 (1999)), Hida presented numerical results indicating that the Haldane phase of the Heisenberg antiferromagnetic spin-1 chain is stable against bond randomness, for box distributions of the bond strength, even when the box distribution stretches to zero bond strength. The author thus concluded that the Haldane phase is stable against bond randomness for any distribution of the bond strength, no matter how broad. In this Comment, we (i) point out that the randomness distributions studied in this Letter do not represent the broadest possible distributions, and therefore these numerical results do not lead to the conclusion that the Haldane phase is stable against any randomness; and (ii) provide a semiquantitative estimate of the critical randomness beyond which the Haldane phase yields to the Random Singlet phase, in a specific class of random distribution functions for the bond strength.Comment: A comment on PRL 83, 3297 (1999). One pag

Percolation Transition in the random antiferromagnetic spin-1 chain

We give a physical description in terms of percolation theory of the phase transition that occurs when the disorder increases in the random antiferromagnetic spin-1 chain between a gapless phase with topological order and a random singlet phase. We study the statistical properties of the percolation clusters by numerical simulations, and we compute exact exponents characterizing the transition by a real-space renormalization group calculation.Comment: 9 pages, 4 encapsulated Postscript figures, REVTeX 3.

Global unions: chasing the dream or building the reality?

This article takes as its theme the global restructuring of capital and its impact on worker organization. It argues for a reassertion of class in any analysis of global solidarity, and assesses the opportunities and barriers to effective global unionization. Rooted in the UK experience, the article analyzes the impact of the European social dimension on trade unions, before taking the discussion into a global dimension. It concludes by suggesting that there are reasons for cautious optimism in terms of solidarity building, despite difficult historical legacies and the common replacement of action with rhetoric

Comparison between disordered quantum spin 1/2 chains

We study the magnetic properties of two types of one dimensional XX spin 1/2 chains. The first type has only nearest neighbor interactions which can be either antiferromagnetic or ferromagnetic and the second type which has both nearest neighbor and next nearest neighbor interactions, but only antiferromagnetic in character. We study these systems in the presence of low transverse magnetic fields both analytically and numerically. Comparison of results show 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.Comment: 7 page

Ground State and Magnetization Process of the Mixture of Bond-Alternating and Uniform S=1/2 Antiferromagnetic Heisenberg Chains

The mixture of bond-alternating and uniform S=1/2 antiferromagnetic Heisenberg chains is investigated by the density matrix renormalization group method. The ground state magnetization curve is calculated and the exchange parameters are determined by fitting to the experimentally measured magnetization curve of \CuCl$_{2x}$Br$_{2(1-x)}$($\gamma$-pic)$_2$. The low field behavior of the magnetization curve and low temperature behavior of the magnetic susceptibility are found to be sensitive to whether the bond-alternation pattern (parity) is fixed all over the sample or randomly distributed. The both quantities are compatible with the numerical results for the random parity model.Comment: 5 pages, 7 figures. Final and enlarged version accepted for publication in J. Phys. Soc. Jp

Dynamics and Transport in Random Antiferromagnetic Spin Chains

We present the first results on the low-frequency dynamical and transport properties of random antiferromagnetic spin chains at low temperature ($T$). We obtain the momentum and frequency dependent dynamic structure factor in the Random Singlet (RS) phases of both spin-1/2 and spin-1 chains, as well as in the Random Dimer phase of spin-1/2 chains. We also show that the RS phases are unusual `spin-metals' with divergent low-frequency conductivity at T=0, and follow the spin conductivity through `metal-insulator' transitions tuned by the strength of dimerization or Ising anisotropy in the spin-1/2 case, and by the strength of disorder in the spin-1 case.Comment: 4 pages (two-column format). Presentation substantially revised to accomodate new result

Ground state of the random-bond spin-1 Heisenberg chain

Stochastic series expansion quantum Monte Carlo is used to study the ground state of the antiferromagnetic spin-1 Heisenberg chain with bond disorder. Typical spin- and string-correlations functions behave in accordance with real-space renormalization group predictions for the random-singlet phase. The average string-correlation function decays algebraically with an exponent of -0.378(6), in very good agreement with the prediction of $-(3-\sqrt{5})/2\simeq -0.382$, while the average spin-correlation function is found to decay with an exponent of about -1, quite different from the expected value of -2. By implementing the concept of directed loops for the spin-1 chain we show that autocorrelation times can be reduced by up to two orders of magnitude.Comment: 9 pages, 10 figure

Real Space Renormalization Group Study of the S=1/2 XXZ Chains with Fibonacci Exchange Modulation

Ground state properties of the S=1/2 antiferromagnetic XXZ chain with Fibonacci exchange modulation are studied using the real space renormalization group method for strong modulation. The quantum dynamical critical behavior with a new universality class is predicted in the isotropic case. Combining our results with the weak coupling renormalization group results by Vidal et al., the ground state phase diagram is obtained.Comment: 9 pages, 9 figure