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International Journal of Modern Physics C

IMPURITY BOND EFFECT ON THE ANTIFERROMAGNETIC ISING-LIKE CHAIN

Makoto Kaburagi, TAKAO MORIWAKI, Tomotoshi Nishino, Takashi Tonegawa

Published Jun 1, 1996• 0 citations
Publisher

Abstract

We investigate the effect of an impurity bond on low-lying excited states of the antiferromagnetic Ising-like chain in terms of domain-wall excitations, using an analytical method and a numerical method. The fundamental difference between the chains with even and odd numbers of spins is discussed.
DOI
10.1142/s0129183196000417

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Low-lying excited states of the spin-1 antiferromagnetic Heisenberg chain with an impurity bond are investigated in terms of domain-wall excitations by means of analytical methods as well as a method of numerical diagonalization. It is shown that 1) the impurity bond brings about a massive triplet mode in the Haldane gap, 2) the triplet state comprises three of the four ground states of an open chain, 3) the excited states with the domain wall trapped at the impurity bond, including the massive triplet mode, exhibit a Néel-type configuration of the magnetic moment around the impurity bond. On the basis of the present results, we propose a new energy versus magnetic-field diagram.
Low-lying excited states of the spin-1 antiferromagnetic Heisenberg chain with an impurity bond are investigated in terms of domain-wall excitations by means of analytical methods as well as a method of numerical diagonalization.It is shown that 1) the impurity bond brings about a massive triplet mode in the Haldane gap, 2) the triplet state comprises three of the four ground states of an open chain, 3) the excited states with the domain wall trapped at the impurity bond, including the massive triplet mode, exhibit a Néel-type configuration of the magnetic moment around the impurity bond.On the basis of the present results, we propose a new energy versus magnetic-field diagram.
We explore low-lying excited states as well as the ground state of the antiferromagnetic S=1 bond-alternating chain with an S=1/2 impurity spin. For the case where the ground-state phase of the host system is the Haldane phase, we review a numerical analysis of the electron-spin-resonance experimental results on the NENP:Cu2+ system. For the case where the ground-state phase of the host system is the dimer phase, on the other hand, we calculate, using the exact-diagonalization method, the dependences of the energy differences between the ground and low-lying excited states upon both the impurity-host exchange constant and the single-ion-type anisotropy constant, and also calculate, using the density-matrix renormalization-group method, the external-magnetic-field dependence of the impurity-spin magnetizaion in the ground state. In these calculations, we keep the NTENP:Cu2+ system in mind to choose the value of the bond-alternation parameter. We find that a few low-lying excited states which are expected from the valence-bond-solid picture appear as the impurity states in the energy gap between the singlet ground and triplet first-excited states (the dimer gap). Furthermore, for certain values of the above constants, we find that the impurity-spin magnetizaion shows a clear jump at a magnetic field which is in the dimer-gap region or in the magnetization-plateau region of the host system, and also that the impurity-spin magnetizaion has a magnetic-field region where it decreases as a function of the magnetic field.
Low-lying excited states as well as the ground state of the spin-1 antiferro- magnetic Heisenberg chain with a spin-1/2 impurity are investigated by means of a variational method and a method of numerical diagonalization. It is shown that 1) the impurity spin brings about massive modes in the Haldane gap, 2) when the the impurity-host coupling is sufficiently weak, the phenomenological Hamiltonian used by Hagiwara {\it et al.} in the analysis of ESR experimental results for NENP containing a small amount of spin-1/2 Cu impurities is equivalent to a more realistic Hamiltonian, as far as the energies of the low-lying states are concerned, 3) the results obtained by the variational method are in semi-quantitatively good agreement with those obtained by the numerical diagonalization.
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The linear chain XXZ spin- (1)/(2) Hamiltonian is mapped onto a model where the local degrees of freedom are domain walls between opposite antiferromagnetic domains. The domain-wall Hamiltonian is solved within the simplest Hartree–Fock approximation with results in very good agreement with the exact solution in the antiferromagnetic regime. The location of ordered and disordered (critical) phases is correct and low-lying excitations are well described and easily interpreted in terms of domain walls. Our domain-wall version of the original Hamiltonian is shown to provide the natural framework for a physical understanding of this system in the antiferromagnetic regime.