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Modern Physics Letters A

Quantum Monte Carlo Simulations of Adulteration Effect on Bond Alternating Spin =1/2 Chain

Peng Zhang, Zhaoxin Xu, He-Ping Ying, Jianhui Dai, P. R. Crompton

Published Mar 28, 2007• 1 citation
Publisher

Abstract

The S =1/2 Heisenberg chain with bond alternation and randomness of antiferromagnetic (AFM) and ferromagnetic (FM) interactions is investigated by quantum Monte Carlo simulations of loop/cluster algorithm. Our results have shown interesting finite temperature magnetic properties of this model. The relevance of our study to former investigation results is discussed.

DOI
10.1142/s0217732307023341

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The S =1/2 Heisenberg chain with bond alternation and randomness of antiferromagnetic (AFM) and ferromagnetic (FM) interactions is investigated by quantum Monte Carlo simulations of loop/cluster algorithm. Our results have shown interesting finite temperature magnetic properties of this model. The relevance of our study to former investigation results is discussed.
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An S=1∕2S=1∕2S=1∕2 ferromagnetic (F) and antiferromagnetic (AF) random alternating Heisenberg quantum spin chain model is investigated in connection to its realization compound ${(\mathrm{C}{\mathrm{H}}_{3})}_{2}\mathrm{C}\mathrm{H}\mathrm{N}{\mathrm{H}}_{3}\mathrm{Cu}{({\mathrm{Cl}}_{x}{\mathrm{Br}}_{1\ensuremath{-}x})}_{3}$. The exchange interaction bonds consist of alternating strong F-AF random bonds and weak uniform AF bonds. Using the quantum Monte Carlo method we have found that the excitation energy gap closes and the uniform AF order becomes critical in the intermediate-concentration region. This finding explains the experimental observation of the magnetic transition by considering weak interchain interactions. The present results suggest that uniform AF order survives even in the presence of randomly located ferromagnetic bonds. This may be an exotic quantum effect.
Thermodynamic properties of spin=1/2 two-leg ladders with alternating chains including ferromagnetic and antiferromagnetic interactions are discussed on the basis of the numerical results obtained by quantum Monte Carlo simulations. As well as the role of exchange interaction of rungs, the essential role of the bond alternation in the chain on ladder systems is investigated in connection with the appearance of characteristic properties in magnetic susceptibilities and heat capacities. Furthermore, quantum effects on the ground-state energy are obtained. On the basis of calculated results, the relationship between singlet dimer phases and Haldane states is discussed.
A possibility of the uniform antiferromagnetic order is pointed out in an S=1/2 ferromagnetic (F) - antiferromagnetic (AF) random alternating Heisenberg quantum spin chain compound: (CH_3)_2 CHNH_3 Cu(Cl_x Br_{1-x})_3. The system possesses the bond alternation of strong random bonds that take +/- 2J and weak uniform AF bonds of -J. In the pure concentration limits, the model reduces to the AF-AF alternation chain at x=0 and to the F-AF alternation chain at x=1. The nonequilibrium relaxation of large-scale quantum Monte Carlo simulations exhibits critical behaviors of the uniform AF order in the intermediate concentration region, which explains the experimental observation of the magnetic phase transition. The present results suggest that the uniform AF order may survive even in the presence of the randomly located ferromagnetic bonds.
We investigate the low-temperature properties of the spin-1 antiferromagnetic Heisenberg chain with bond alternation by the quantum Monte Carlo method (loop algorithm). The strength of bond alternation at the gapless point is estimated as ${\ensuremath{\delta}}_{c}=0.2595\ifmmode\pm\else\textpm\fi{}0.0005.$ We confirm numerically that the low-temperature properties at the gapless point are consistent with field-theoretical predictions. The numerical results are compared with those of the spin-1/21/21/2 antiferromagnetic Heisenberg chain and recent experimental results for $[{{\mathrm{Ni}(333\ensuremath{-}\mathrm{t}\mathrm{e}\mathrm{t})(\mathrm{\ensuremath{\mu}}\ensuremath{-}\mathrm{N}}_{3}){}}_{n}]({\mathrm{ClO}}_{4}{)}_{n}$ [$333\ensuremath{-}\mathrm{t}\mathrm{e}\mathrm{t}=\mathrm{t}\mathrm{e}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{e}$ ${N,N}^{\ensuremath{'}}$-bis(3-aminopropyl)-1,3-propanediamine].
Ground state properties, dispersion relations and scaling behaviour of spin gap of a bond alternating spin-1 2 anisotropic Heisenberg chain have been studied where the exchange interactions on alternate bonds are ferromagnetic (FM) and antiferromagnetic (AFM) in two separate cases.The resulting models separately represent nearest neighbour (NN) AFM-AFM and AFM-FM bond alternating chains.Ground state energy has been estimated analytically by using both bond operator and Jordan-Wigner representations and numerically by using exact diagonalization.Dispersion relations, spin gap and several ground state orders have been obtained.Dimer order and string orders are found to coexist in the ground state.Spin gap is found to develop as soon as the non-uniformity in alternating bond strength is introduced in the AFM-AFM chain which further remains non-zero for the AFM-FM chain.This spin gap along with the string orders attribute to the Haldane phase.The Haldane phase is found to exist in most of the anisotropic region similar to the isotropic point.