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

The Free Energy and the Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field

Hiroaki Nakamura, Minoru Takahashi

A nonlinear susceptibilities (the third derivative of a magnetization $m_S$ by a magnetic field $h$ ) of the $S$ =1/2 ferromagnetic Heisenberg chain and the classical Heisenberg chain are calculated at low temperatures $T.$ In both chains the nonlinear susceptibilities diverge as $T^{-6}$ and a linear susceptibilities diverge as $T^{-2}.$ The arbitrary spin $S$ Heisenberg ferromagnet $[$ ${\cal H} = \sum_{i=1}^{N} \{ - J{\bf S}_{i} {\bf S}_{i+1} - (h/S) S_{i}^{z} \}$ $(J>0),$ $]$ has a scaling relation between $m_S,$ $h$ and $T:$ $m_S(T,h) = F( S^2 Jh/T^2).$ The scaling function $F(x)$ =(2 $x$ /3)-(44 $x^{3}$ /135) + O( $x^{5}$ ) is common to all values of spin $S.$ A nonlinear susceptibilities (the third derivative of a magnetization $m_S$ by a magnetic field $h$ ) of the $S$=1/2 ferromagnetic Heisenberg chain and the classical Heisenberg chain are calculated at low temperatures $T.$ In both chains the nonlinear susceptibilities diverge as $T^{-6}$ and a linear susceptibilities diverge as $T^{-2}.$ The arbitrary spin $S$ Heisenberg ferromagnet $[$ ${\cal H} = \sum_{i=1}^{N} \{ - J{\bf S}_{i} {\bf S}_{i+1} - (h/S) S_{i}^{z} \}$ $(J>0),$ $]$ has a scaling relation between $m_S,$ $h$ and $T:$ $m_S(T,h) = F( S^2 Jh/T^2).$ The scaling function $F(x)$=(2$x$/3)-(44$x^{3}$/135) + O($x^{5}$) is common to all values of spin $S.$

arXiv:cond-mat/9401074Journal of the Physical Society of JapanJul 15, 199420 citations

The Heisenberg picture

Series in atomic and molecular physics/Series in atomic molecular physicsDec 1, 20030 citations

Cavity Heisenberg-spin-chain quantum battery

Fu-Quan Dou, Hang Zhou, Jianan Sun

We propose a cavity Heisenberg-spin-chain (CHS) quantum battery (QB) with the long-range interactions and investigate its charging process. The performance of the CHS QB is substantially improved compared to the Heisenberg spin chain (HS) QB. When the number of spins $N\ensuremath{\gg}1$, the quantum advantage $\ensuremath{\alpha}$ of the QB's maximum charging power can be obtained, which approximately satisfies the superlinear scaling relation ${P}_{\mathrm{max}}\ensuremath{\propto}{N}^{\ensuremath{\alpha}}$. The CHS QB can approach $\ensuremath{\alpha}=2$ by optimizing the parameters. We find that the maximum stored energy of the CHS QB has a critical phenomenon. By analyzing the Wigner function, von Neumann entropy, and logarithmic negativity, we demonstrate that entanglement can be a necessary ingredient for QB to store more energy, but not sufficient.We propose a cavity Heisenberg-spin-chain (CHS) quantum battery (QB) with the long-range interactions and investigate its charging process. The performance of the CHS QB is substantially improved compared to the Heisenberg spin chain (HS) QB. When the number of spins $N\ensuremath{\gg}1$, the quantum advantage $\ensuremath{\alpha}$ of the QB's maximum charging power can be obtained, which approximately satisfies the superlinear scaling relation ${P}_{\mathrm{max}}\ensuremath{\propto}{N}^{\ensuremath{\alpha}}$. The CHS QB can approach $\ensuremath{\alpha}=2$ by optimizing the parameters. We find that the maximum stored energy of the CHS QB has a critical phenomenon. By analyzing the Wigner function, von Neumann entropy, and logarithmic negativity, we demonstrate that entanglement can be a necessary ingredient for QB to store more energy, but not sufficient.

arXiv:2206.10181Physical Review ASep 14, 2022102 citations

The Heisenberg picture

Institute of Physics eBooksNov 26, 20040 citations

A nonlinear susceptibilities (the third derivative of a magnetization

m_S

by a magnetic field

h

) of the

S

=1/2 ferromagnetic Heisenberg chain and the classical Heisenberg chain are calculated at low temperatures

T.

In both chains the nonlinear susceptibilities diverge as

T^{-6}

and a linear susceptibilities diverge as

T^{-2}.

The arbitrary spin

S

Heisenberg ferromagnet

[

{\cal H} = \sum_{i=1}^{N} \{ - J{\bf S}_{i} {\bf S}_{i+1} - (h/S) S_{i}^{z} \}

(J>0),

]

has a scaling relation between

m_S,

h

and

T:

m_S(T,h) = F( S^2 Jh/T^2).

The scaling function

F(x)

=(2

x

/3)-(44

x^{3}

/135) + O(

x^{5}

) is common to all values of spin

S.