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Journal of Applied Physics

Effects of randomness in gapped antiferromagnetic quantum spin chains

Kun Yang, R. A. Hyman, R. N. Bhatt, S. M. Girvin

Published Apr 15, 1996• 27 citations
Publisher

Abstract

The effects of bond randomness are studied for spin chains with excitation gaps in the pure case. Systems with enforced topological structure like the spin-1/2 chain with enforced dimerization and spin-1 chain in the Haldane gapped phase appear very stable against randomness. On the other hand, systems with spontaneously generated topological order like the spin-1/2 chain with spontaneous dimerization are found to be unstable even for weak randomness despite the gap.

DOI
10.1063/1.361312

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The effects of bond randomness are studied for spin chains with excitation gaps in the pure case. Systems with enforced topological structure like the spin-1/2 chain with enforced dimerization and spin-1 chain in the Haldane gapped phase appear very stable against randomness. On the other hand, systems with spontaneously generated topological order like the spin-1/2 chain with spontaneous dimerization are found to be unstable even for weak randomness despite the gap.
The effect of bond randomness on the spin-gapped ground state of the spin-1 bond-alternating antiferromagnetic Heisenberg chain is discussed. By using the loop cluster quantum Monte Carlo method, we investigate the stability of topological order in terms of the recently proposed twist order parameter [M. Nakamura and S. Todo: Phys. Rev. Lett. 89 (2002) 077204]. It is observed that the dimer phases as well as the Haldane phase of the spin-1 Heisenberg chain are robust against a weak randomness, though the valence-bond-solid-like topological order in the latter phase is destroyed by introducing a disorder stronger than the critical value.
We study the random antiferromagnetic spin-1 chain by mapping to a random dimerized spin-1/2 chain with antiferromagnetic and ferromagnetic bonds and applying an asymptotically exact real space renormalization procedure. We find that the chain undergoes an impurity driven second order phase transition from the Haldane phase to the random singlet phase as the bond distribution broadens. In the Haldane phase and near the critical point, there is a Griffiths region in which the excitation gap is filled and the magnetic susceptibility diverges in a nonuniversal manner. The correlation length critical exponent is $\ensuremath{\nu}\ensuremath{\approx}2.3$.
By using Lanczos exact diagonalization and quantum Monte Carlo combined with stochastic analytic continuation, we study the dynamical properties of the S = 1 antiferromagnetic Heisenberg chain with different strengths of bond disorder. In the weak disorder region, we find weakly coupled bonds which can induce additional low-energy excitation below the one-magnon mode. As the disorder increases, the average Haldane gap closes at δ Δ ∼ 0.5 with more and more low-energy excitations coming out. After the critical disorder strength δ c ∼ 1, the system reaches a random-singlet phase with prominent sharp peak at ω = 0 and broad continuum at ω > 0 of the dynamic spin structure factor. In addition, we analyze the distribution of random spin domains and numerically find three kinds of domains hosting effective spin-1/2 quanta or spin-1 sites in between. These “spins” can form the weakly coupled long-range singlets due to quantum fluctuation which contribute to the sharp peak at ω = 0.
The S=1/2 ferromagnetic (F) - antiferromagnetic (AF) random alternating Heisenberg quantum spin chain is investigated by the quantum Monte Carlo method. The randomness is only present on the strong bonds taking values of ±2J randomly, and the weak bonds are uniformly antiferromagnetic with J. The model corresponds to the quasi one-dimensional compound, (CH3)2CHNH3Cu(Clx, Br1-x)3, whose ground state interpolates the Haldane state of the F-AF alternating spin chain at x=1 and the singlet-dimer state of the AF-AF alternating spin chain at x=0. The nonequilibrium relaxation function of the staggered magnetic susceptibility exhibits algebraic divergence in the intermediate region of 0.44 ≪ x ≪ 0.87, which explains the experimental observation of the magnetic phase transition. The results suggest that the antiferromagnetic order becomes critical by the randomness of the bond distributions even in the presence of the rich ferromagnetic bonds.
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.