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arXiv:cond-mat/0607786 · Journal of the Physical Society of Japan

Bond-Dilution-Induced Quantum Phase Transitions in Heisenberg Antiferromagnets

Chitoshi Yasuda, Synge Todo, Hajime Takayama

Published Nov 27, 2006• 5 citations
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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.

DOI
10.1143/jpsj.75.124704

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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.
Dilution effects on spin-1/2 quantum Heisenberg antiferromagnets with a non-magnetic spin-gapped ground state are studied by means of the quantum Monte Carlo simulation. In the site-diluted system, an antiferromagnetic long-range order (AF-LRO) is induced at an infinitesimal concentration of dilution due to an effective coupling ̃Jmn between induced magnetic moments. In the bond-diluted case, on the other hand, the AF-LRO is not induced up to a certain concentration of dilution due to singlet pairs reformed by an AF coupling ̃J af between the edge spins of the diluted bond through the two-dimensional shortest paths. The competition between ̃Jmn and ̃J af yields peculiar phenomena in the bond-diluted system.
Effects of the site dilution on spin-gapped Heisenberg antiferromagnets with S=12S=\frac{1}{2}S=21​ and S=1S=1S=1 on a square lattice of coupled dimerized chains are investigated by means of the quantum Monte Carlo method. It is found that effective magnetic moments induced around the diluted sites exhibit the antiferromagnetic long-range order in the medium of spin-singlet pairs. Their microscopic structure is examined in detail and important roles of higher dimensionality other than one in the phenomenon are discussed.
Quantum phase transition of site-diluted and bond-diluted Heisenberg antiferromagnets on square lattices is studied. By using the novel continuous-time loop algorithm, we perform quantum Monte Carlo simulations on quite larger lattices at extremely lower temperatures than the previous numerical studies. It is found that the antiferromagnetic long-range order at T = 0 persists so long as a cluster of magnetic sites percolates, that is, the critical concentration is equal to the classical percolation threshold, in both of the site-diluted and bond-diluted cases. Furthermore, we find that some critical exponents, such as the magnetization exponent β, are non-classical and strongly depend on the spin size S. On the other hand, we show that the correlation-length exponent ν is universal and is equal to the classical value (ν=4/3).
The effects of regular S=1 dilution of S=1/2 isotropic antiferromagnetic chain are investigated by the quantum Monte Carlo loop/cluster algorithm. Our numerical results show that there are two kinds of ground-state phases which alternate with the variation of S1=1S^1=1S1=1 concentration. When the effective spin of a unit cell is half-integer, the ground state is ferrimagnetic with gapless energy spectrum and the magnetism becomes weaker with decreasing of the S1S^1S1 concentration ρ=1/Mρ= 1/Mρ=1/M. While it is integer, a non-magnetic ground state with gaped spectrum emerges and the gap gradually becomes narrowed as fitted by a relation of Δ≈1.25ρΔ\approx 1.25\sqrtρΔ≈1.25ρ​.
The two-dimensional antiferromagnetic S=1/2S=1/2S=1/2 Heisenberg model with random site dilution is studied using quantum Monte Carlo simulations. Ground-state properties of the largest connected cluster on $L\ifmmode\times\else\texttimes\fi{}L$ lattices, with L up to 64, are calculated at the classical percolation threshold. In addition, clusters with a fixed number Nc{N}_{c}Nc​ of spins on an infinite lattice at the percolation density are studied for Nc{N}_{c}Nc​ up to 1024. The disorder averaged sublattice magnetization per spin extrapolates to the same nonzero infinite-size value for both types of clusters. Hence, the percolating clusters, which are fractal with dimensionality d=91/48,d=91/48,d=91/48, have antiferromagnetic long-range order. This implies that the order-disorder transition driven by site dilution occurs exactly at the percolation threshold and that the exponents are classical. The same conclusion is reached for the bond-diluted system. The full sublattice magnetization versus site dilution curve is obtained in terms of a decomposition into a classical geometrical factor and a factor containing all the effects of quantum fluctuations. The spin stiffness is shown to obey the same scaling as the conductivity of a random resistor network.
The two-dimensional antiferromagnetic S=1/2 Heisenberg model with random bond dilution is studied using quantum Monte Carlo simulation at the percolation threshold (50% of the bonds removed). Finite-size scaling of the staggered structure factor averaged over the largest connected clusters of sites on L*L lattices shows that long-range order exists within the percolating fractal clusters in the thermodynamic limit. This implies that the order-disorder transition driven by bond-dilution occurs exactly at the percolation threshold and that the exponents are classical. This result should apply also to the site-diluted system.