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Progress of Theoretical Physics Supplement

AnS=1/2 Impurity Spin in the AntiferromagneticS=1 Bond-Alternating Chain

Nobuyuki Ogawa, Toshiya Hikihara, Makoto Kaburagi, Takashi Tonegawa

Published Jan 1, 2002• 0 citations

Abstract

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.

DOI: 10.1143/ptps.145.156

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Makoto Kaburagi, Takashi Tonegawa, Minkyu Kang

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Journal of the Physical Society of Japan•Jan 2, 2003•1 citation

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 antiferromagnetic Heisenberg chain with a spin-1/2 impurity are studied by means of a method of numerical diagonalization. The isotropic nearest-neighbor exchange coupling plus the uniaxial single-ion-type anisotropy energy is assumed for the host-system Hamiltonian. The energy differences between the ground state and the low-lying excited states, which appear in the Haldane gap, are estimated in the thermodynamic limit. The results are used to analyze the electron-spin-resonance experimental data on Ni(C

_2

H

_8

N

_2

)

_2

NO

_2

(ClO

_4

), abbreviated NENP, containing a small amount of spin-1/2 Cu

^{2+}

impurities. It is found that in this system, the impurity-host

\bigl(

Cu

^{2+}

-Ni

^{2+}

\bigr)

coupling is ferromagnetic and its magnitude is about 5

\,

\% of the magnitude of the host-host

\bigl(

Ni

^{2+}

-Ni

^{2+}

\bigr)

coupling.

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.

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 report spin wave and density-matrix renormalization-group (DMRG) studies of the ground and low-lying excited states of uniform and dimerized alternating spin chains. The DMRG procedure is also employed to obtain low-temperature thermodynamic properties of the system. The ground state of a 2N spin system with spin-1 and spin- alternating from site to site and interacting via an antiferromagnetic exchange is found to be ferrimagnetic with total spin

{\mathrm{s}}_{\mathrm{G}}

=N/2 from both DMRG and spin wave analysis. Both the studies also show that there is a gapless excitation to a state with spin

{\mathrm{s}}_{\mathrm{G}}

-1 and a gapped excitation to a state with spin

{\mathrm{s}}_{\mathrm{G}}

+1. Surprisingly, the correlation length in the ground state is found to be very small from both the studies for this gapless system. For this very reason, we show that the ground state can be described by a variational ansatz of the product type. DMRG analysis shows that the chain is susceptible to a conditional spin-Peierls' instability. The DMRG studies of magnetization, magnetic susceptibility (\ensuremath{\chi}), and specific heat show strong magnetic-field dependence. The product \ensuremath{\chi}T shows a minimum as a function of temperature (T) at low-magnetic fields and the minimum vanishes at high-magnetic fields. This low-field behavior is in agreement with earlier experimental observations. The specific heat shows a maximum as a function of temperature and the height of the maximum increases sharply at high-magnetic fields. It is hoped that these studies will motivate experimental studies at high-magnetic fields.

Low-lying excited states of the spin-1 antiferromagnetic Heisenberg chain with a spin- S ( S >1) impurity are investigated by means of variational method. It is shown that (1) the phenomenological Hamiltonian which may be useful in the analysis of the experimental results can be derived from the usual Hamiltonian, (2) the origin of the anisotropy in the phenomenological Hamiltonian can be explained from the results obtained by the analytical method, (3) the impurity spin brings about a massive mode in the Haldane gap, (4) the energy levels of the massive mode can be classified into four multiples corresponding to the states with the total spin quantum S = S +1, S and S -1 coupled to triplet of host-system and the state with S = S coupled to the singlet of host-system.