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arXiv:cond-mat/0606269

Order from Disorder in the Two-Dimensional Kondo-Necklace

Wolfram Brenig

Published Jun 11, 2006• 0 citations
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Abstract

We analyze the effects of site-dilution disorder on the thermodynamic properties of the two-dimensional Kondo necklace using finite-temperature stochastic series expansion. Results will be discussed for the dependence on dilution concentration, temperature, and Kondo exchange-coupling strength of the uniform susceptibility, the staggered structure factor, and the Chakravarty-Halperin-Nelson ratio. Dilution is shown to induce effective free-spin clusters in the gapped phase of the clean system with a low-temperature Curie constant renormalized below 1/4. Furthermore, dilution is demonstrated to generate antiferromagnetic order in the quantum disordered phase of the clean system, i.e. order-from-disorder. In turn, the quantum critical point of the clean system, separating an antiferromagnetic from a paramagnetic dimerized state at a critical Kondo exchange-coupling strength $J_{c}\approx1.4$ is suppressed. Finally, speculations on a renormalized classical behavior in the dilution induced ordered phase are stated.

DOI
10.48550/arxiv.cond-mat/0606269

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We analyze the effects of site-dilution disorder on the thermodynamic properties of the two-dimensional Kondo necklace using finite-temperature stochastic series expansion. Results will be discussed for the dependence on dilution concentration, temperature, and Kondo exchange-coupling strength of the uniform susceptibility, the staggered structure factor, and the Chakravarty-Halperin-Nelson ratio. Dilution is shown to induce effective free-spin clusters in the gapped phase of the clean system with a low-temperature Curie constant renormalized below 1/4. Furthermore, dilution is demonstrated to generate antiferromagnetic order in the quantum disordered phase of the clean system, i.e. order-from-disorder. In turn, the quantum critical point of the clean system, separating an antiferromagnetic from a paramagnetic dimerized state at a critical Kondo exchange-coupling strength Jc≈1.4J_{c}\approx1.4Jc​≈1.4 is suppressed. Finally, speculations on a renormalized classical behavior in the dilution induced ordered phase are stated.
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We obtain the phase diagram and thermodynamic behavior of the Kondo necklace model for arbitrary dimensions ddd using a representation for the localized and conduction electrons in terms of local Kondo singlet and triplet operators. A decoupling scheme on the double time Green's functions yields the dispersion relation for the excitations of the system. We show that in $d\ensuremath{\geqslant}3$, there is an antiferromagnetically ordered state at finite temperatures terminating at a quantum critical point (QCP). In two dimensions, long-range magnetic order occurs only at T=0T=0T=0. The line of N\'eel transitions for d>2d>2d>2 varies with the distance to the quantum critical point QCP $\ensuremath{\mid}g\ensuremath{\mid}$ as ${T}_{N}\ensuremath{\propto}{\ensuremath{\mid}g\ensuremath{\mid}}^{\ensuremath{\psi}}$, where the shift exponent $\ensuremath{\psi}=1∕(d\ensuremath{-}1)$. In the paramagnetic side of the phase diagram, the spin gap behaves as $\ensuremath{\Delta}\ensuremath{\approx}\sqrt{\ensuremath{\mid}g\ensuremath{\mid}}$ for $d\ensuremath{\geqslant}3$, consistent with the value z=1z=1z=1 found for the dynamical critical exponent. We also find in this region a power law temperature dependence in the specific heat for ${k}_{B}T⪢\ensuremath{\Delta}$ and along the non-Fermi-liquid trajectory. For ${k}_{B}T⪡\ensuremath{\Delta}$, in the so-called Kondo spin liquid phase, the thermodynamic behavior is dominated by an exponential temperature dependence.
Ground state properties of the randomly diluted two-dimensional Heisenberg antiferromagnet are discussed. Quantum Monte Carlo (stochastic series expansion) data for L×L lattices, with L up to 64, are extrapolated to infinite size for dilution fractions p between 0 (clean system) and p* (the percolation threshold). The sublattice magnetization is calculated using a decomposition into a classical and a quantum mechanical factor, which are evaluated separately. The quantum mechanical factor (the sublattice magnetization of the largest connected cluster of magnetic sites) remains finite at the percolation threshold, implying that the dilution driven order-disorder transition is a classical percolation transition. The spin stiffness is calculated using the winding number fluctuations.
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Abstract In this paper, we study the thermodynamic properties of spin-1/2 antiferromagnetic Heisenberg ladders by means of the stochastic series expansion quantum Monte Carlo technique. This includes the thermal properties of the specific heat, uniform and staggered susceptibilities, spin gap, and structure factor. Our numerical simulations are probed over a large ensemble of random realizations in a wide range of disorder strengths r, from the clean ( r=0r=0r=0 r = 0 ) case up to the diluted ( r→1r \rightarrow 1r→1 r → 1 ) limit, and for selected choices of number of legs LyL_yLy​ L y per site. Our results show some interesting phenomena, like the presence of crossing points in the temperature plane for both the specific heat and uniform susceptibility curves which appear to be universal in r, as well as a variable dependence of the spin gap in the amount of disorder upon increasing LyL_yLy​ L y . Graphical 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.