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arXiv:cond-mat/0201443 · Physical review. B, Condensed matter

Interplay between quasiperiodicity and disorder in quantum spin chains in a magnetic field

Marcelo Arlego

Published Aug 29, 2002• 8 citations
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Abstract

We study the interplay between disorder and a quasiperiodic coupling array in an external magnetic field in a spin-$\frac{1}{2}$ $\mathrm{XXZ}$ 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 $\mathrm{XX}$ chains. Spontaneous susceptibility properties are also studied, finding a logarithmic behavior similar to the homogeneously disordered case.

DOI
10.1103/physrevb.66.052419

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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 study the interplay between a (quasi) periodic coupling array and an external magnetic field in a spin-12\frac{1}{2}21​ XXZ\mathrm{XXZ}XXZ chain. A new class of magnetization plateau is obtained by means of Abelian bosonization methods which gives rise to a sufficient quantization condition. The investigation of magnetic phase diagrams via exact diagonalization of finite clusters finds a complete agreement with the continuum treatment in a variety of situations.
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.
In the framework of the exactly solvable model, using nonperturbative methods, the temperature and magnetic field behavior of the NMR relaxation rate (and low-energy dynamical structure factor) for the antiferromagnetic Heisenberg spin-1/2 chain with magnetic impurities is calculated. For a single magnetic impurity, totally screened at low temperatures by spinons of the chain, the critical exponents, which determine the low-temperature and magnetic field behavior, get renormalized. For the finite concentration of impurities with the random distribution of the impurity-chain coupling the weak disorder in the distribution does not produce essential changes to the dynamical structure factor. Contrary, the strong disorder yields drastically different behavior of the low-energy dynamical characteristics, comparing to the homogeneous chain. Our results are generic, and they qualitatively agree in limiting cases with the results of perturbative calculations for disordered spin chains and with the data of experiments on quasi-one-dimensional spin compounds.
Exact results for the thermodynamic properties of ensembles of magnetic impurities with randomly distributed host-impurity couplings in the quantum antiferromagnetic Heisenberg model are presented. Exact calculations are done for arbitrary values of temperature and external magnetic field. We have shown that for strong disorder the quenching of the impurity moments is absent. For weak disorder the screening persists, but with the critical non-Fermi-liquid behaviors of the magnetic susceptibility and specific heat. A comparison with disordered Kondo effect experiments in dirty metallic alloys is performed.