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arXiv:cond-mat/0007205 · Physical Review Letters

Random Bond XXZ Chains with Modulated Couplings

D. C. Cabra, Alessandro De Martino, Marcelo D. Grynberg, S. Peysson, Pierre Pujol

Published Nov 27, 2000• 19 citations
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Abstract

The magnetization behavior of q-periodic antiferromagnetic spin- 1/2 Heisenberg chains under uniform magnetic fields is investigated in a background of disorder exchange distributions. By means of both real space decimation procedures and numerical diagonalizations in XX chains, it is found that for binary disorder the magnetization exhibits wide plateaus at values of 1+2(p-1)/q, where p is the disorder strength. In contrast, no spin gaps are observed in the presence of continuous exchange distributions. We also study the magnetic susceptibility at low magnetic fields.

DOI
10.1103/physrevlett.85.4791

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The magnetization behavior of q-periodic antiferromagnetic spin- 1/2 Heisenberg chains under uniform magnetic fields is investigated in a background of disorder exchange distributions. By means of both real space decimation procedures and numerical diagonalizations in XX chains, it is found that for binary disorder the magnetization exhibits wide plateaus at values of 1+2(p-1)/q, where p is the disorder strength. In contrast, no spin gaps are observed in the presence of continuous exchange distributions. We also study the magnetic susceptibility at low magnetic fields.
We report results of theoretical investigations on the effect of doping and quenched disorder on the occurrence of plateaux in the magnetization curve of 1D systems with periodic modulations in the couplings.For single q-merized Hubbard chains, doping is shown to affect the position at which plateaux appear, leading to the emergence of plateaux at irrational values of the magnetization.For random bond antiferromagnetic Heisenberg chains with periodically modulated bond distributions, disorder generically removes the plateau structure, except in the case of discrete probability distributions.In the latter case, wide plateaux emerge at values of the magnetization dependent on the strength of disorder.
We reportresultsoftheoreticalinvestigationsonthe eectofdopingandquencheddisor- derontheoccurrenceofplateauxinthemagnetizationcurveof1Dsystemswithperiodicmodulations inthe couplings. Forsingleq-merizedHubbardchains,dopingisshownto aectthe positionatwhich plateaux appear, leading to the emergence of plateaux atirrationalvalues of the magnetization. For random bond antiferromagnetic Heisenberg chains with periodically modulated bond distributions, disorder generically removes the plateau structure, except in the case of discrete probability distri- butions. In the latter case, wide plateaux emerge at values of the magnetization dependent on the strength of disorder.
We consider the spin-1/2 Heisenberg chain with alternating spin exchange in the presence of additional modulation of exchange on odd bonds with period 3. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective XXZ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In the absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped phase into the only one gapless Lüttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to [Formula: see text] and [Formula: see text] of the saturation value. These phases reveal themselves also in the magnetization curve as plateaus at corresponding values of magnetization. As a result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless, and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.
The multiple reentrant quantum phase transitions in the S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg chains with random bond alternation in the magnetic field are investigated by the density matrix renormalization group method combined with the interchain mean field approximation. It is assumed that the odd-th bond is antiferromagnetic with strength JJJ and even-th bond can take the values ${\JS}$ and ${\JW}$ $ ({\JS} > J > {\JW} > 0)$ randomly with probability ppp and 1−p1-p1−p, respectively. The pure version (p=0p=0p=0 and p=1p=1p=1) of this model has a spin gap but exhibits a field induced antiferromagnetism in the presence of interchain coupling if Zeeman energy due to the magnetic field exceeds the spin gap. For 0<p<10 < p < 10<p<1, the antiferromagnetism is induced by randomness at small field region where the ground state is disordered due to the spin gap in the pure case. At the same time, this model exhibits randomness induced plateaus at several values of magnetization. The antiferromagnetism is destroyed on the plateaus. As a consequence, we find a series of reentrant quantum phase transitions between the transverse antiferromagnetic phases and disordered plateau phases with the increase of the magnetic field for moderate strength of interchain coupling. Above the main plateaus, the magnetization curve consists of a series of small plateaus and the jumps between them, It is also found that the antiferromagnetism is induced by infinitesimal interchain coupling at the jumps between the small plateaus. We conclude that this antiferromagnetism is supported by the mixing of low lying excited states by the staggered interchain mean field even though the spin correlation function is short ranged in the ground state of each chain.
We study the interplay between disorder and a quasiperiodic coupling array in an external magnetic field in a spin-12\frac{1}{2}21​ XXZ\mathrm{XXZ}XXZ chain. A simple real space decimation argument is used to estimate the magnetization values where plateaux show up. The latter are in good agreement with exact diagonalization results on fairly long XX\mathrm{XX}XX chains. Spontaneous susceptibility properties are also studied, finding a logarithmic behavior similar to the homogeneously disordered case.
We have studied the presence of plateaus on the low-temperature magnetization of an antiferromagnetic spin-1 chain, as an external uniform magnetic field is varied. A crystal-field interaction is present in the model and the exchange constants follow a random quenched (Bernoulli or Gaussian) distribution. Using a transfer-matrix technique we calculate the largest Lyapunov exponent and, from it, the magnetization at low temperatures as a function of the magnetic field, for different values of the crystal field and the width of the distributions. For the Bernoulli distribution, the number of plateaus increases, with respect to the uniform case [Litaiff et al., Solid State Commun. 147, 494 (2008)] and their presence can be linked to different ground states, when the magnetic field is varied. For the Gaussian distributions, the uniform scenario is maintained, for small widths, but the plateaus structure disappears as the width increases.