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

Identifying a correlated spin fluctuation in an entangled spin chain subject to a quantum phase transition

Kaoru Shimizu, 康弘都倉

This paper presents a theoretical framework for analyzing the quantum fluctuation properties of a quantum spin chain subject to a quantum phase transition. We can quantify the fluctuation properties by examining the correlation between the fluctuations of two neighboring spins subject to the quantum uncertainty. To do this, we first compute the reduced density matrix \ensuremath{\rho} of the spin pair from the ground state |\ensuremath{\Psi}⟩ of a spin chain, and then identify the quantum correlation part ${\ensuremath{\rho}}_{q}$ embedded in \ensuremath{\rho}. If the spin chain is translationally symmetric and characterized by a nearest-neighbor two-body spin interaction, we can determine uniquely the form of ${\ensuremath{\rho}}_{q}$ as $W|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}\ensuremath{\langle}\mathrm{\ensuremath{\Phi}}|$ with the weight $W$ $\ensuremath{\le}1$, and quantify the fluctuation properties using the two-spin entangled state $|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}$. We demonstrate the framework for a transverse-field quantum Ising spin chain and indicate its validity for more general spin chain models.This paper presents a theoretical framework for analyzing the quantum fluctuation properties of a quantum spin chain subject to a quantum phase transition. We can quantify the fluctuation properties by examining the correlation between the fluctuations of two neighboring spins subject to the quantum uncertainty. To do this, we first compute the reduced density matrix \ensuremath{\rho} of the spin pair from the ground state |\ensuremath{\Psi}⟩ of a spin chain, and then identify the quantum correlation part ${\ensuremath{\rho}}_{q}$ embedded in \ensuremath{\rho}. If the spin chain is translationally symmetric and characterized by a nearest-neighbor two-body spin interaction, we can determine uniquely the form of ${\ensuremath{\rho}}_{q}$ as $W|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}\ensuremath{\langle}\mathrm{\ensuremath{\Phi}}|$ with the weight $W$ $\ensuremath{\le}1$, and quantify the fluctuation properties using the two-spin entangled state $|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}$. We demonstrate the framework for a transverse-field quantum Ising spin chain and indicate its validity for more general spin chain models.

Physical Review EDec 28, 20150 citations

Quantum Spin Chains

Jill C. Bonner, Henk W. J. Blöte, Hans Beck +1 more

Springer series in solid-state sciencesJan 1, 198146 citations

W

$\ensuremath{\le}1$, and quantify the fluctuation properties using the two-spin entangled state $|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}$. We demonstrate the framework for a transverse-field quantum Ising spin chain and indicate its validity for more general spin chain models.