Bond-Dilution-Induced Quantum Phase Transitions in Heisenberg Antiferromagnets

Abstract

Bond-dilution effects on the ground state of the square-lattice antiferromagnetic Heisenberg model, consisting of coupled bond-alternating chains, are investigated by means of the quantum Monte Carlo simulation. It is found that, when the ground state of the non-diluted system is a non-magnetic state with a finite spin gap, a sufficiently weak bond dilution induces a disordered state with a mid gap in the original spin gap, and under a further stronger bond dilution an antiferromagnetic long-range order emerges. While the site-dilution-induced long-range order is induced by an infinitesimal concentration of dilution, there exists a finite critical concentration in the case of bond dilution. We argue that this essential difference is due to the occurrence of two types of effective interactions between induced magnetic moments in the case of bond dilution, and that the antiferromagnetic long-range-ordered phase does not appear until the magnitudes of the two interactions become comparable.KEYWORDS: dilution-induced antiferromagnetic long-range order, quantum Monte Carlo simulation, quantum phase transition, non-magnetic impurity, spin-Peierls compound 2 J. Phys. Soc. Jpn.

Correlations in quantum spin ladders with site and bond dilution

“…7(c), see also Refs. 21,22). Such correlations appear because the spacing between diluted rung bonds decreases, and hence the couplings between LMs belonging to different rungs become of the same order of J (eff) rung .…”

Position of Effective Spins Induced by Dilution in Two-Dimensional Spin-Peierls Systems

“…In the bond-diluted system with the A-type distortion, the reformation of a spin-singlet pair is known to occur from a previous work on the bond-alternated system. 16) As shown in Fig. 11(a), two effective spins are induced at the ends of the right removed bond, and an AF effective interaction with a strength of J ′2 (1 + ∆) arises between effective spins through the interchain interaction.…”

“…12,13) Bond-dilution effects in the twodimensional antiferromagnetic (AF) Heisenberg model consisting of bond-alternating chains have been studied by performing quantum Monte Carlo (QMC) simulations. [14][15][16] When a bond is removed in the dimerized state, effective spins are induced around two sites at the * E-mail address:cyasuda@sci.u-ryukyu.ac.jp edges of the removed bond. There are two effective interactions between the effective spins.…”

“…The AFLRO does not appear until the magnitudes of the two interactions become comparable. 16) In such diluted systems, the effective spins are induced near the diluted sites or bonds. However, experimental results that contradict the numerical results have been reported for the bond-disorder system of CuGe 1−x Si x O 3 .…”

“…From Cu nuclear quadrupole resonance (NQR) data, it was concluded that effective spins are not induced near the impurities. 17) As mentioned above, the theoretical studies on dilution effects in the two-dimensional AF Heisenberg model consisting of bond-alternating chains concluded that effective spins were induced near diluted parts; 11,16) these studies, however, assumed that the pattern of lattice distortion was the same as that in a nondiluted system up to a certain impurity concentration. Thus, we need to consider the lattice degree of freedom to investigate the effects of the positions of the induced effective spins on the AFLRO.…”