We discuss zero-temperature quantum spin chains in a uniform magnetic field, with axial symmetry. For integer or half-integer spin, $S$ , the magnetization curve can have plateaus and we argue that the magnetization per site $m$ is topologically quantized as $n(S\ensuremath{-}m)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{integer}$ at the plateaus, where $n$ is the period of the ground state. We also discuss conditions for the presence of the plateau at those quantized values. For $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2$ and $m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ , we study several models and find two distinct types of massive phases at the plateau. One of them is argued to be a ``Haldane gap phase'' for half-integer $S$ .We discuss zero-temperature quantum spin chains in a uniform magnetic field, with axial symmetry. For integer or half-integer spin, $S$, the magnetization curve can have plateaus and we argue that the magnetization per site $m$ is topologically quantized as $n(S\ensuremath{-}m)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{integer}$ at the plateaus, where $n$ is the period of the ground state. We also discuss conditions for the presence of the plateau at those quantized values. For $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2$ and $m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$, we study several models and find two distinct types of massive phases at the plateau. One of them is argued to be a ``Haldane gap phase'' for half-integer $S$.

arXiv:cond-mat/9610168Physical Review LettersMar 10, 1997710 citations

A field theory route towards critical spin chains

Germán Sierra

Journal of Physics A Mathematical and TheoreticalNov 15, 20160 citations

Impurity-Bond Effect on the Spin-1 Antiferromagnetic Heisenberg Chain

Makoto Kaburagi, Isao Hrada, Takashi Tonegawa

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.

Journal of the Physical Society of JapanJan 15, 19940 citations

Construction and study of exact ground states of quantum spin chains

M. Fannes, Bruno Nachtergaele, Reinhard F. Werner

Brazilian Journal of PhysicsJan 1, 19890 citations

Impurity-Bond Effect on the Spin-1 Antiferromagnetic Heisenberg Chain

Makoto Kaburagi, Isao Harada, Takashi Tonegawa

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.

arXiv:cond-mat/9304040Journal of the Physical Society of JapanJun 15, 199328 citations

We discuss zero-temperature quantum spin chains in a uniform magnetic field, with axial symmetry. For integer or half-integer spin,

S

, the magnetization curve can have plateaus and we argue that the magnetization per site

m

is topologically quantized as $n(S\ensuremath{-}m)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{integer}$ at the plateaus, where

n

is the period of the ground state. We also discuss conditions for the presence of the plateau at those quantized values. For

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2

and

m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2

, we study several models and find two distinct types of massive phases at the plateau. One of them is argued to be a ``Haldane gap phase'' for half-integer

S