Excitation Spectrum of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain

Kazuo Hida

Published Jan 1, 1994• 23 citations

Abstract

Related papers

Kazuo Hida

arXiv:cond-mat/9404017Journal of the Physical Society of JapanJul 15, 199428 citations

Crossover of spectral features from Dimerized to Haldane behavior in alternating antiferromagnetic-ferromagnetic spin-half chains

Weihong Zheng, Chris J. Hamer, Rajiv R. P. Singh

arXiv:cond-mat/0605370May 15, 20060 citations

A kind of ferromagnetic-antiferromagnetic alternating spin chain equivalent to the mixed spin Heisenberg chain

Jianjun Jiang, Yang Cui-hong, Yongjun Liu

Acta Physica SinicaJan 1, 20120 citations

Elementary excitations of Heisenberg ferrimagnetic spin chains

Shoji Yamamoto, S. Brehmer, H.-J. Mikeska

arXiv:cond-mat/9710332Physical review. B, Condensed matterJun 1, 1998114 citations

Size-dependent low-energy excitations in an alternating spin-1/spin- 12 antiferromagnetic chain: Spin-wave theory and density-matrix renormalization-group studies

Sasmita Mohakud, Swapan Kumar Pati, Seiji Miyashita

Physical Review BJul 27, 200715 citations

Magnetic excitation spectrum of dimerized antiferromagnetic chains

Götz Silvester Uhrig, Heinz J. Schulz

arXiv:cond-mat/9606001Physical review. B, Condensed matterOct 1, 1996170 citations

Excitation Spectrum of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain

Kazuo Hida

Published Jan 1, 1994• 23 citations

OpenAlex

Abstract

Related papers

Excitation Spectrum of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain

Kazuo Hida

The natural explanation of the excitation spectrum of the spin-1 antiferromagnetic Heisenberg chain is given from the viewpoint of the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain. The energy spectrum of the latter is calculated with fixed momentum $k$ by numerical diagonalization of finite size systems. It consists of a branch of propagating triplet pair (triplet wave) and the continuum of multiple triplet waves for weak ferromagnetic coupling. As the ferromagnetic coupling increases, the triplet wave branch is absorbed in the continuum for small $k$ , reproducing the characteristics of the spin-1 antiferromagnetic Heisenberg chain.The natural explanation of the excitation spectrum of the spin-1 antiferromagnetic Heisenberg chain is given from the viewpoint of the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain. The energy spectrum of the latter is calculated with fixed momentum $k$ by numerical diagonalization of finite size systems. It consists of a branch of propagating triplet pair (triplet wave) and the continuum of multiple triplet waves for weak ferromagnetic coupling. As the ferromagnetic coupling increases, the triplet wave branch is absorbed in the continuum for small $k$, reproducing the characteristics of the spin-1 antiferromagnetic Heisenberg chain.

arXiv:cond-mat/9404017Journal of the Physical Society of JapanJul 15, 199428 citations

Crossover of spectral features from Dimerized to Haldane behavior in alternating antiferromagnetic-ferromagnetic spin-half chains

Weihong Zheng, Chris J. Hamer, Rajiv R. P. Singh

We calculate the excitation spectrum and spectral weights of the alternating antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange couplings $J$ and $-|λ|J$ as a power series in $λ$ . For small $|λ|$ , the gapped one-particle spectrum has a maximum at $k=0$ and there is a rich structure of bound (and anti-bound) states below (and above) the 2-particle continuum. As $|λ|$ is increased past unity the spectrum crosses over to the Haldane regime, where the peak shifts away from $k=0$ , the one particle states merge with the bottom of the continuum near $k=0$ , and the spectral weights associated with the one-particle states become very small. Extrapolation of the spectrum to large $|λ|$ confirms that the ground state energy and excitation gap map onto those of the spin-one chain.We calculate the excitation spectrum and spectral weights of the alternating antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange couplings $J$ and $-|λ|J$ as a power series in $λ$. For small $|λ|$, the gapped one-particle spectrum has a maximum at $k=0$ and there is a rich structure of bound (and anti-bound) states below (and above) the 2-particle continuum. As $|λ|$ is increased past unity the spectrum crosses over to the Haldane regime, where the peak shifts away from $k=0$, the one particle states merge with the bottom of the continuum near $k=0$, and the spectral weights associated with the one-particle states become very small. Extrapolation of the spectrum to large $|λ|$ confirms that the ground state energy and excitation gap map onto those of the spin-one chain.

arXiv:cond-mat/0605370May 15, 20060 citations

A kind of ferromagnetic-antiferromagnetic alternating spin chain equivalent to the mixed spin Heisenberg chain

Jianjun Jiang, Yang Cui-hong, Yongjun Liu

By using the method of exact diagonalization, the properties of the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain are investigated. The spin-spin correlation, the sublattice magnetizations, the spin excitation spectrum and the magnetization curve of the model are calculated and compared with the corresponding properties of the mixed spin chain. The results show that the behaviors of the alternating Heisenberg chain are equivalent to those of the mixed spin chain when the ratio of antiferromagnetic to ferromagnetic coupling strength is very small. So, the properties of the mixed spin chain can be analyzed by using the spin-1/2 ferromagnetic-antiferromagnetic-antiferromagnetic alternating Heisenberg chain.By using the method of exact diagonalization, the properties of the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain are investigated. The spin-spin correlation, the sublattice magnetizations, the spin excitation spectrum and the magnetization curve of the model are calculated and compared with the corresponding properties of the mixed spin chain. The results show that the behaviors of the alternating Heisenberg chain are equivalent to those of the mixed spin chain when the ratio of antiferromagnetic to ferromagnetic coupling strength is very small. So, the properties of the mixed spin chain can be analyzed by using the spin-1/2 ferromagnetic-antiferromagnetic-antiferromagnetic alternating Heisenberg chain.

Acta Physica SinicaJan 1, 20120 citations

Elementary excitations of Heisenberg ferrimagnetic spin chains

Shoji Yamamoto, S. Brehmer, H.-J. Mikeska

We numerically investigate elementary excitations of the Heisenberg alternating-spin chains with two kinds of spins, 1 and $1/2,$ antiferromagnetically coupled to each other. Employing a recently developed efficient Monte Carlo technique as well as an exact-diagonalization method, we verify the spin-wave argument that the model exhibits two distinct excitations from the ground state which are gapless and gapped. The gapless branch shows a quadratic dispersion in the small-momentum region, which is of the ferromagnetic type. With the intention of elucidating the physical mechanism of both excitations, we make a perturbation approach from the decoupled-dimer limit. The gapless branch is directly related to spin 1's, while the gapped branch originates from cooperation of the two kinds of spins.We numerically investigate elementary excitations of the Heisenberg alternating-spin chains with two kinds of spins, 1 and $1/2,$ antiferromagnetically coupled to each other. Employing a recently developed efficient Monte Carlo technique as well as an exact-diagonalization method, we verify the spin-wave argument that the model exhibits two distinct excitations from the ground state which are gapless and gapped. The gapless branch shows a quadratic dispersion in the small-momentum region, which is of the ferromagnetic type. With the intention of elucidating the physical mechanism of both excitations, we make a perturbation approach from the decoupled-dimer limit. The gapless branch is directly related to spin 1's, while the gapped branch originates from cooperation of the two kinds of spins.

arXiv:cond-mat/9710332Physical review. B, Condensed matterJun 1, 1998114 citations

Size-dependent low-energy excitations in an alternating spin-1/spin- 12 antiferromagnetic chain: Spin-wave theory and density-matrix renormalization-group studies

Sasmita Mohakud, Swapan Kumar Pati, Seiji Miyashita

We study the properties of the ground state and the low-lying excited states of an alternating spin-1 and spin- $\frac{1}{2}$ antiferromagnetic chain with ferromagnetic next-nearest-neighbor coupling with a variety of methods, namely, spin-wave analysis, density-matrix renormalization-group (DMRG) method, and exact-diagonalization method. The ground state of this model with $2N$ spins is ferrimagnetic with the total spin ${S}_{G}=N∕2$ for all parameter values. In the long chain limit, a gapless excitation is found with characteristics of goldstone mode of the ferromagnetic order with total spin $S={S}_{G}\ensuremath{-}1$. The lowest gapped excitation, however, exists in the total spin $S={S}_{G}+1$ sector. Interestingly, we find that with the increase in ferromagnetic coupling, spin-wave gapped excitation becomes lower than the massless mode for the large wave numbers. Correspondingly, from DMRG analysis we find that the excitation in the total spin $S={S}_{G}+1$ is lower than that in the total spin $S={S}_{G}\ensuremath{-}1$ when the size of the chain is short and the ferromagnetic interaction is large. Characteristics of these excitations are also reflected in the low temperature thermodynamic quantities, where the low-energy properties are strongly affected by the system size and the coupling strength.We study the properties of the ground state and the low-lying excited states of an alternating spin-1 and spin-$\frac{1}{2}$ antiferromagnetic chain with ferromagnetic next-nearest-neighbor coupling with a variety of methods, namely, spin-wave analysis, density-matrix renormalization-group (DMRG) method, and exact-diagonalization method. The ground state of this model with $2N$ spins is ferrimagnetic with the total spin ${S}_{G}=N∕2$ for all parameter values. In the long chain limit, a gapless excitation is found with characteristics of goldstone mode of the ferromagnetic order with total spin $S={S}_{G}\ensuremath{-}1$. The lowest gapped excitation, however, exists in the total spin $S={S}_{G}+1$ sector. Interestingly, we find that with the increase in ferromagnetic coupling, spin-wave gapped excitation becomes lower than the massless mode for the large wave numbers. Correspondingly, from DMRG analysis we find that the excitation in the total spin $S={S}_{G}+1$ is lower than that in the total spin $S={S}_{G}\ensuremath{-}1$ when the size of the chain is short and the ferromagnetic interaction is large. Characteristics of these excitations are also reflected in the low temperature thermodynamic quantities, where the low-energy properties are strongly affected by the system size and the coupling strength.

Physical Review BJul 27, 200715 citations

Magnetic excitation spectrum of dimerized antiferromagnetic chains

Götz Silvester Uhrig, Heinz J. Schulz

Motivated by recent measurements on CuGe ${\mathrm{O}}_{3}$ , the spectrum of magnetic excitations of an antiferromagnetic $S=\frac{1}{2}$ chain with alternating coupling strength is investigated. Wave-vector-dependent magnons and a continuum with square-root behavior at the band edges are found. The spectral density of the continua is calculated. Spin-rotation symmetry fixes the gap of the continuum to be twice the elementary magnon gap. This is in excellent agreement with experimental results. The existence of (anti)bound states of two magnons is predicted: below the continuum a singlet and a triplet, above the continuum a quintuplet.Motivated by recent measurements on CuGe${\mathrm{O}}_{3}$, the spectrum of magnetic excitations of an antiferromagnetic $S=\frac{1}{2}$ chain with alternating coupling strength is investigated. Wave-vector-dependent magnons and a continuum with square-root behavior at the band edges are found. The spectral density of the continua is calculated. Spin-rotation symmetry fixes the gap of the continuum to be twice the elementary magnon gap. This is in excellent agreement with experimental results. The existence of (anti)bound states of two magnons is predicted: below the continuum a singlet and a triplet, above the continuum a quintuplet.

arXiv:cond-mat/9606001Physical review. B, Condensed matterOct 1, 1996170 citations

k

by numerical diagonalization of finite size systems. It consists of a branch of propagating triplet pair (triplet wave) and the continuum of multiple triplet waves for weak ferromagnetic coupling. As the ferromagnetic coupling increases, the triplet wave branch is absorbed in the continuum for small

k

, reproducing the characteristics of the spin-1 antiferromagnetic Heisenberg chain.

We calculate the excitation spectrum and spectral weights of the alternating antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange couplings

J

and

-|λ|J

as a power series in

λ

. For small

|λ|

, the gapped one-particle spectrum has a maximum at

k=0

and there is a rich structure of bound (and anti-bound) states below (and above) the 2-particle continuum. As

|λ|

is increased past unity the spectrum crosses over to the Haldane regime, where the peak shifts away from

k=0

, the one particle states merge with the bottom of the continuum near

k=0

, and the spectral weights associated with the one-particle states become very small. Extrapolation of the spectrum to large

|λ|

confirms that the ground state energy and excitation gap map onto those of the spin-one chain.

We numerically investigate elementary excitations of the Heisenberg alternating-spin chains with two kinds of spins, 1 and

1/2,

antiferromagnetically coupled to each other. Employing a recently developed efficient Monte Carlo technique as well as an exact-diagonalization method, we verify the spin-wave argument that the model exhibits two distinct excitations from the ground state which are gapless and gapped. The gapless branch shows a quadratic dispersion in the small-momentum region, which is of the ferromagnetic type. With the intention of elucidating the physical mechanism of both excitations, we make a perturbation approach from the decoupled-dimer limit. The gapless branch is directly related to spin 1's, while the gapped branch originates from cooperation of the two kinds of spins.

We study the properties of the ground state and the low-lying excited states of an alternating spin-1 and spin-

\frac{1}{2}

antiferromagnetic chain with ferromagnetic next-nearest-neighbor coupling with a variety of methods, namely, spin-wave analysis, density-matrix renormalization-group (DMRG) method, and exact-diagonalization method. The ground state of this model with

2N

spins is ferrimagnetic with the total spin

{S}_{G}=N∕2

for all parameter values. In the long chain limit, a gapless excitation is found with characteristics of goldstone mode of the ferromagnetic order with total spin $S={S}_{G}\ensuremath{-}1$. The lowest gapped excitation, however, exists in the total spin

S={S}_{G}+1

sector. Interestingly, we find that with the increase in ferromagnetic coupling, spin-wave gapped excitation becomes lower than the massless mode for the large wave numbers. Correspondingly, from DMRG analysis we find that the excitation in the total spin

S={S}_{G}+1

is lower than that in the total spin $S={S}_{G}\ensuremath{-}1$ when the size of the chain is short and the ferromagnetic interaction is large. Characteristics of these excitations are also reflected in the low temperature thermodynamic quantities, where the low-energy properties are strongly affected by the system size and the coupling strength.

Motivated by recent measurements on CuGe

{\mathrm{O}}_{3}

, the spectrum of magnetic excitations of an antiferromagnetic

S=\frac{1}{2}

chain with alternating coupling strength is investigated. Wave-vector-dependent magnons and a continuum with square-root behavior at the band edges are found. The spectral density of the continua is calculated. Spin-rotation symmetry fixes the gap of the continuum to be twice the elementary magnon gap. This is in excellent agreement with experimental results. The existence of (anti)bound states of two magnons is predicted: below the continuum a singlet and a triplet, above the continuum a quintuplet.