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International Journal of Modern Physics B

QUANTUM MONTE CARLO STUDY ON RANDOM BOND MIXED-SPIN CHAIN

Hongwei Fan, Zhaoxin Xu, He-Ping Ying

Published Sep 30, 2007• 0 citations
Publisher

Abstract

The effects of bond randomness on the quantum mixed-spin chain 1-1-1/2-1/2 are investigated by a quantum Monte Carlo study. We find that around the critical point of original pure system, quantum Griffiths phases appears, and its region is enlarged with increasing of bond randomness. Moreover, the critical behavior of the original quantum critical point has been changed by the randomness.

DOI
10.1142/s0217979207045402

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The effects of bond randomness on the quantum mixed-spin chain 1-1-1/2-1/2 are investigated by a quantum Monte Carlo study. We find that around the critical point of original pure system, quantum Griffiths phases appears, and its region is enlarged with increasing of bond randomness. Moreover, the critical behavior of the original quantum critical point has been changed by the randomness.
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The ground-state and thermodynamic properties of quantum mixed-spin chains of1/2-1/2-1-1and 3/2-3/2-1-1are investigated by a quantum Monte Carlo simulation with the loop-cluster algorithm. For 1/2-1/2-1-1 chain, we find it has two phases separated by an energy-gap vanishing point in the ground-state. For 3/2-3/2-1-1 chain, the numerical results show two energy-gap vanishing points isolated by different phases in its ground-state. Our calculations indicate that all these ground state phases can be understood by means of valence-bond-solid picture, and the thermodynamic behavior at finite temperatures is continuous as a function of parameterα=J2/J1.
The ground-state and thermodynamic properties of quantum mixed-spin chains of1/2-1/2-1-1and 3/2-3/2-1-1are investigated by a quantum Monte Carlo simulation with the loop-cluster algorithm. For 1/2-1/2-1-1 chain, we find it has two phases separated by an energy-gap vanishing point in the ground-state. For 3/2-3/2-1-1 chain, the numerical results show two energy-gap vanishing points isolated by different phases in its ground-state. Our calculations indicate that all these ground state phases can be understood by means of valence-bond-solid picture, and the thermodynamic behavior at finite temperatures is continuous as a function of parameterα=J2/J1.
Combining quantum Monte Carlo simulations with the maximum entropy method, we study the dynamical structure factor S(k,ω)S(k,ω)S(k,ω) of spin-1/2 antiferromagnetic Heisenberg chains with various random bond distributions. We emphasize the crossover behavior in the dynamical properties from pure chain to disorder-dominated random singlet phase due to bond randomness. For the distribution corresponding to the infinite randomness fixed point, S(k,ω)S(k,ω)S(k,ω) develops broad non-spinon excitations as well as the random-singlet peak near (k,ω)=(π,0)(k, ω) = (π, 0)(k,ω)=(π,0), consistent with the known results obtained by the real-space renormalization group method. For weak disorder, however, we find clear signature of spinon excitations, reminiscent of pure spin chains, blurred by disorder. We discuss the implication for experiments on random-bond antiferromagnetic spin chains, realizable, e.g., in BaCu2_22​(Six_xx​Ge1−x_{1-x}1−x​)2_22​O7_77​.
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.
For the two dimensional random bond disordered Ising ferromagnet, we measured bulk data of the magnetic susceptibility (χχχ) and correlation length (ξξξ) up to ξ≃536ξ\simeq 536ξ≃536, with the use of a novel finite size scaling Monte Carlo technique. Our data are exclusively consistent with normal power-law critical behaviors with only one singular point at criticality, disproving the existence of Griffiths singularity even in an extremely deep scaling region. The critical exponents of χχχ and ξξξ increase continuously with the strength of disorder.