Randomness-driven Quantum Phase Transition in Bond-alternating Haldane Chain

Abstract

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.KEYWORDS: Haldane chain, bond randomness, quantum phase transitions, random-singlet phase, quantum Monte Carlo, loop algorithm, topological order, twist order parameterDisorder effects on low-dimensional quantum magnets have been investigated extensively in recent theoretical studies. In particular, impurity effects on spin-gapped Heisenberg antiferromagnets 1 have aroused much interest in relation to the impurity-induced antiferromagnetic (AF) long-range order observed experimentally in real materials.2 It has been established by recent numerical simulations 3, 4 that in two dimensions or higher, there are two classes of disorder, that affect spin-gapped states in essentially different ways. Site dilution and bond dilution are representatives of each class. The former induces localized moments around impurity sites. There exist strong correlations between such effective spins retaining the staggeredness with respect to the original lattice, and therefore the AF long-range order emerges by an infinitesimal concentration of dilution. In the bonddilution case, on the other hand, localized moments are always induced in pairs and they form a singlet again by AF interactions through the two-or three-dimensional shortest paths as long as the concentration of bond dilution is smaller than a finite critical value.In one dimension, since quantum fluctuations are much stronger than those in higher-dimensional systems, novel quantum critical phenomena are observed under disorder at the magnitude of coupling constants (bond randomness). Theoretically, the decimation renormalization group (DRG) approaches have achieved great success in predicting rich physics, such as the random-singlet (RS) phase for spin-1 2 chains.5-7 Recently, this technique has been extended to higher-spin cases, [8][9][10][11] where two of the main debates are on the robustness of the Haldane gap 12 against disorder and on the presence of the spin-1 RS phase. A number of numerical studies have also been carried out [13][14][15][16] to establish a quantitative phase diagram. However, this problem has not been sufficiently clarified yet. One of the main difficulties in simulating random quantum systems is the extremely wide energy scale that has to be taken into account. Another difficulty * Present address: Speech Interface Technology Group, NEC Corporation, Kawasaki 211-8666, Japan. † E-mail address: wistaria@ap.t.u-to...

Disorder-induced phases in theS=1antiferromagnetic Heisenberg chain

“…At the critical point no numerical estimates are available to check analytical RG predictions. We note on recent studies of Griffiths effects 16 in the system with en-forced dimerization 17,18 and related work on the random S = 3/2 and higher spin chains 19,20,21 . In this paper, our aim is to study the low-energy properties of the random S = 1 chain by the DMRG method.…”

Strong disorder RG approach of random systems

“…The effects of enforced dimerization on random S = 1 chains have also been studied via real space RG in [109], and numerically in [35] : in the phase diagram in the plane (dimerization δ,randomness R), the critical point at (δ = 0, R c ) now becomes multicritical. This kind of multicritical point has been further discussed in [110].…”

Renormalization-Group Investigation of the S = 1 Random Antiferromagnetic Heisenberg Chain

“…ψ = 0.5 was found at δ = 1.0 also in a series of recent QMC and SDRG studies. 12,14,15,26 Thus, the properties of the RSP at the critical point and for different strength of disorder seem to be coherent as it is indicated in…”

“…The Griffiths phase can be further divided, at δ = δ 1 , into nonsingular and singular phases. GRG provides reasonable estimates on the phase boundaries by applying finite-size scaling analysis, see Fig.3, δ 1 = 0.40 (15) and δ c = 1.00 (15). From a theoretical point of view, the GRG scheme is well-established; from a numerical point of view, the data from GRG technique is well-justified.…”

“…In S = 1/2 chain, Ma and Dasgupta introduced a RG technique, 4,6 with which it was possible to point out that any small amount of disorder triggers the random-singlet phase (RSP) where spins in arbitrarily large distance are coupled in singlets. In S = 1 chain, 7,8,9,10,11,12,13,14,15 only sufficiently large disorder is able to change the pure system properties.…”