Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Springer proceedings in physics

Crossover Between the Haldane Gap Phase and the Dimer Phase in the Spin 1/2 Alternating Heisenberg Chain

Kazuo Hida

Published Jan 1, 1992• 2 citations
Publisher
DOI
10.1007/978-3-642-84821-6_30

Related papers

Investigation of the Haldane State and the Singlet Dimer State Formed in Alternating Heisenberg Chains with S=1/2

浩貴 真中

•Jan 1, 2001•0 citations

Haldane Phase and Large-D Phase of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain with On-Site Anisotropy

清美 岡本, Kiyomi Okamoto

•Jan 1, 1993•0 citations

Crossover between the Haldane-gap phase and the dimer phase in the spin-1/2 alternating Heisenberg chain

Kazuo Hida

The ground-state properties of the spin-1/2 Heisenberg chain, which has two exchange couplings (J>J') alternatingly, are studied. This model interpolates the spin-1 antiferromagnetic Heisenberg chain (AFHC) (J'\ensuremath{\rightarrow}-\ensuremath{\infty}, J>0), the dimerized spin-1/2 AFHC (J'\ensuremath{\simeq}J>0), and the uniform spin-1/2 AFHC (J'=J>0) continuously. The string order introduced by den Nijs--Rommelse and Tasaki changes continuously through the Haldane phase and the dimer phase to vanish at J=J'. It is at a maximum for J'=0. This implies that the string order is related to the local singlet correlation in terms of the spin-1/2 model. The lowest excitation can be regarded as the renormalized triplet wave. The reversal of the anisotropy effect on the excitation spectrum of the spin-1 AFHC is also explained in a intuitive way based on this picture.

Physical review. B, Condensed matter•Feb 1, 1992•274 citations

Coupled cluster study of the dimer state of the spin-1/2 alternating Heisenberg chain

Jianjun Jiang, Yongjun Liu

Physica B Condensed Matter•May 19, 2008•3 citations

Appearance of a gapless phase over the intermediate region between the Haldane phase and the singlet dimer phase in random alternating Heisenberg chains (CH3)2CHNH3Cu(ClxBr1−x)3

Hirotaka Manaka, Isao Yamada, Hiroko Aruga Katori

The isomorphous compounds $({\mathrm{CH}}_{3}{)}_{2}{\mathrm{CHNH}}_{3}{\mathrm{CuCl}}_{3}$ and $({\mathrm{CH}}_{3}{)}_{2}{\mathrm{CHNH}}_{3}{\mathrm{CuBr}}_{3}$ consist of ferromagnetic-antiferromagnetic and antiferromagnetic-antiferromagnetic alternating Heisenberg chains with $S=1/2,$ respectively. The ground state is therefore regarded as the Haldane state in the former and the singlet dimer state in the latter. To clarify the effect of bond randomness on the Haldane state as well as on the singlet dimer state, the magnetic states of the random alternating Heisenberg chains $({\mathrm{CH}}_{3}{)}_{2}{\mathrm{CHNH}}_{3}\mathrm{Cu}({\mathrm{Cl}}_{x}{\mathrm{Br}}_{1\ensuremath{-}x}{)}_{3},$ i.e., mixed systems of the two compounds mentioned above, were investigated. From magnetic susceptibility and specific heat measurements, it was confirmed that a gapless phase appears over the intermediate region $0.44<x<0.87.$ At the two boundaries, i.e., the boundary between the Haldane phase and the gapless phase and that between the gapless phase and the singlet dimer phase, the energy gap abruptly becomes zero. This study clarifies that bond randomness wipes out the energy gap in both the Haldane state and the singlet dimer state, when the strength of bond randomness exceeds a certain value.

Physical review. B, Condensed matter•Feb 14, 2001•41 citations

Haldane gap in the spin- ½ double chain Heisenberg antiferromagnet

Kazuo Hida

Journal of Magnetism and Magnetic Materials•Feb 1, 1992•2 citations
The ground-state properties of the spin-1/2 Heisenberg chain, which has two exchange couplings (J>J') alternatingly, are studied. This model interpolates the spin-1 antiferromagnetic Heisenberg chain (AFHC) (J'\ensuremath{\rightarrow}-\ensuremath{\infty}, J>0), the dimerized spin-1/2 AFHC (J'\ensuremath{\simeq}J>0), and the uniform spin-1/2 AFHC (J'=J>0) continuously. The string order introduced by den Nijs--Rommelse and Tasaki changes continuously through the Haldane phase and the dimer phase to vanish at J=J'. It is at a maximum for J'=0. This implies that the string order is related to the local singlet correlation in terms of the spin-1/2 model. The lowest excitation can be regarded as the renormalized triplet wave. The reversal of the anisotropy effect on the excitation spectrum of the spin-1 AFHC is also explained in a intuitive way based on this picture.
The isomorphous compounds (CH3)2CHNH3CuCl3({\mathrm{CH}}_{3}{)}_{2}{\mathrm{CHNH}}_{3}{\mathrm{CuCl}}_{3}(CH3​)2​CHNH3​CuCl3​ and (CH3)2CHNH3CuBr3({\mathrm{CH}}_{3}{)}_{2}{\mathrm{CHNH}}_{3}{\mathrm{CuBr}}_{3}(CH3​)2​CHNH3​CuBr3​ consist of ferromagnetic-antiferromagnetic and antiferromagnetic-antiferromagnetic alternating Heisenberg chains with S=1/2,S=1/2,S=1/2, respectively. The ground state is therefore regarded as the Haldane state in the former and the singlet dimer state in the latter. To clarify the effect of bond randomness on the Haldane state as well as on the singlet dimer state, the magnetic states of the random alternating Heisenberg chains $({\mathrm{CH}}_{3}{)}_{2}{\mathrm{CHNH}}_{3}\mathrm{Cu}({\mathrm{Cl}}_{x}{\mathrm{Br}}_{1\ensuremath{-}x}{)}_{3},$ i.e., mixed systems of the two compounds mentioned above, were investigated. From magnetic susceptibility and specific heat measurements, it was confirmed that a gapless phase appears over the intermediate region 0.44<x<0.87.0.44<x<0.87.0.44<x<0.87. At the two boundaries, i.e., the boundary between the Haldane phase and the gapless phase and that between the gapless phase and the singlet dimer phase, the energy gap abruptly becomes zero. This study clarifies that bond randomness wipes out the energy gap in both the Haldane state and the singlet dimer state, when the strength of bond randomness exceeds a certain value.