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arXiv:cond-mat/9712252 · Physical Review Letters

Generation of Large Moments in a Spin-1 Chain with Random Antiferromagnetic Couplings

Kun Yang, R. N. Bhatt

Published May 18, 1998• 17 citations
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Abstract

We study the spin-1 chain with nearest neighbor couplings that are rotationally invariant, but include both Heisenberg and biquadratic exchange, with random strengths. We demonstrate, using perturbative renormalization group methods as well as exact diagonalization of clusters, that the system generates ferromagnetic couplings under certain circumstances even when all the bare couplings are antiferromagnetic. This disorder induced instability leads to formation of large magnetic moments at low temperatures, and is a purely quantum mechanical effect that does not have a classical counterpart. The physical origin of this instability, as well as its consequences, are discussed.

DOI
10.1103/physrevlett.80.4562

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We study the spin-1 chain with nearest neighbor couplings that are rotationally invariant, but include both Heisenberg and biquadratic exchange, with random strengths. We demonstrate, using perturbative renormalization group methods as well as exact diagonalization of clusters, that the system generates ferromagnetic couplings under certain circumstances even when all the bare couplings are antiferromagnetic. This disorder induced instability leads to formation of large magnetic moments at low temperatures, and is a purely quantum mechanical effect that does not have a classical counterpart. The physical origin of this instability, as well as its consequences, are discussed.
A random antiferromagnetic spin-1 chain with both Heisenberg and biquadratic nearest neighbor couplings is found to exhibit a novel ferromagnetic-like instability at low energies, if there is competition between the Heisenberg and biquadratic couplings, even though each individual nearest neighbor coupling is such as to produce a singlet ground state for the isolated pair. This instability leads to the generation of ferromagnetic couplings, and thus to the formation of weakly coupled large moments at low temperatures. A perturbative calculation (up to 4th order) is performed to investigate whether such a situation is physically realizable in spin-1 systems.
We have carried out Monte Carlo studies of a random-exchange antiferromagnetic spin-(1/2) chain. For systems with XY-like (anisotropic) and with Heisenberg (isotropic) coupling, our results confirm the existence of a disorder-induced low-temperature (T) divergence in the long-wavelength Sz{S}^{z}Sz-Sz{S}^{z}Sz susceptibility \ensuremath{\chi} which was previously predicted by real-space renormalization-group (RSRG) treatments. Over the finite temperature range studied, these results are consistent with a 1/(T ln2{\mathrm{ln}}^{2}ln2T) behavior of \ensuremath{\chi}, and hence in qualitative agreement with the RSRG results. As in the XY-Heisenberg regime, we also find a disorder-induced enhancement of the low-T susceptibility for a system with Ising-like exchange coupling which, over the finite temperature range studied, is again consistent with RSRG results. However, there are inconsistencies between the RSRG predictions in the Ising-like regime at very low temperatures, and the exact results for the random-exchange Ising chain and the low-temperature behavior of \ensuremath{\chi} in the Ising-like regime may in fact be more complicated than predicted by RSRG. Finally, we also present results for the antiferromagnetic susceptibility and structure factor. For both Heisenberg and Ising-like systems, we find that disorder suppresses the long-range antiferromagnetic correlations at low T.
We study disordered antiferromagnetic spin-12\frac{1}{2}21​ chains with nearest- and further-neighbor interactions using the real-space renormalization-group method. We find that the system supports two different phases, depending on the ratio of the strength between nearest-neighbor and further-neighbor interactions as well the bond randomness strength. For weak further-neighbor coupling the system is in the familiar random singlet phase, while stronger further-neighbor coupling drives the system to a large spin phase similar to that found in the study of random antiferromagnetic-ferromagnetic spin chains. The appearance of the large spin phase in the absence of ferromagnetic coupling is due to the frustration introduced by further-neighboring couplings, and is unique to the disordered chains.
We study the 1D quantum Heisenberg chain with randomly ferromagnetic or antiferromagnetic couplings [a model previously studied by approximate strong-disorder renormalization group (RG)]. We find that, at least for sufficiently large spin S , the ground state has “spin glass” order. The spin waves on top of this state have the dynamical exponent z = 3 / 2 , intermediate between the values z = 1 of the antiferromagnet and z = 2 of the ferromagnet. Density matrix renormalization group (DMRG) simulations are in good agreement with the analytical results for spins S = 1 and S = 3 / 2 . The case S = 1 / 2 shows large finite size effects: We suggest that this case is also ordered, but with a small ordered moment.
We study the one-dimensional Heisenberg spin-1∕21∕21∕2 alternating bond chain in which the nearest neighbor exchange couplings are ferromagnetic (FM) and antiferromagnetic (AF) alternatively. By using exact diagonalization and the density matrix renormalization group method, we discuss how the system approaches the AF uniform spin-1 chain under certain conditions. When the ratio of AF to FM coupling strengths, $\ensuremath{\alpha}$ $(\ensuremath{\alpha}={J}_{AF}∕{J}_{F})$, is very small, physical properties of the alternating bond chain such as spin-spin correlation, the string correlation function, and the spin density coincide with those of the AF uniform spin-1 chain. The edge state problem is discussed in the present model with the small $\ensuremath{\alpha}$ limit. In addition, the Haldane gap of the AF uniform spin-1 chain is four times the gap of the system considered.
The low energy properties of the spin-1/2 random Heisenberg chain with ferromagnetic and antiferromagnetic interactions are studied by means of the density matrix renormalization group (DMRG) and real space renormalization group (RSRG) method for finite chains. The results of the two methods are consistent with each other. The deviation of the gap distribution from that of the random singlet phase and the formation of the large-spin state is observed even for relatively small systems. For a small fraction of the ferromagnetic bond, the effect of the crossover to the random singlet phase on the low temperature susceptibility and specific heat is discussed. The crossover concentration of the ferromagnetic bond is estimated from the numerical data.