The pair-wise thermal entanglement in a four-qubit Heisenberg XXZ chain is investigated to study the role of anisotropy when an external magnetic field is included. It is found that pair-wise entanglement is absent between nearest- and next-nearest neighbouring qubits with anisotropic parameter Δ⩽−1. For two nearest-neighbouring qubits, increasing the parameter can not only induce the entanglement, but also extend the entanglement region in terms of magnetic field B and temperature T . For two next-nearest-neighbouring qubits, increasing anisotropic parameter can shift the location of the entanglement and control the extent of the entanglement in terms of magnetic field at a finite temperature.The pair-wise thermal entanglement in a four-qubit Heisenberg XXZ chain is investigated to study the role of anisotropy when an external magnetic field is included. It is found that pair-wise entanglement is absent between nearest- and next-nearest neighbouring qubits with anisotropic parameter Δ⩽−1. For two nearest-neighbouring qubits, increasing the parameter can not only induce the entanglement, but also extend the entanglement region in terms of magnetic field B and temperature T . For two next-nearest-neighbouring qubits, increasing anisotropic parameter can shift the location of the entanglement and control the extent of the entanglement in terms of magnetic field at a finite temperature.

Chinese Physics LettersOct 26, 20066 citations

Quantum Phase Transition in Dimerized Spin-1/2 Chains

Aparajita Das, Sreeparna Bhadra, Sonali Saha

Quantum phase transition in dimerized antiferromagnetic Heisenberg spin chain has been studied. A staircase structure in the variation of concurrence within strongly coupled pairs with that of external magnetic field has been observed indicating multiple critical points. Emergence of entanglement due to external magnetic field or magnetic entanglement is observed for weakly coupled spin pairs in the same dimer chain. Though closed dimerized isotropic XXX Heisenberg chains with different dimer strengths were mainly explored, analogous studies on open chains as well as closed anisotropic (XX interaction) chains with tilted external magnetic field have also been studied.Quantum phase transition in dimerized antiferromagnetic Heisenberg spin chain has been studied. A staircase structure in the variation of concurrence within strongly coupled pairs with that of external magnetic field has been observed indicating multiple critical points. Emergence of entanglement due to external magnetic field or magnetic entanglement is observed for weakly coupled spin pairs in the same dimer chain. Though closed dimerized isotropic XXX Heisenberg chains with different dimer strengths were mainly explored, analogous studies on open chains as well as closed anisotropic (XX interaction) chains with tilted external magnetic field have also been studied.

arXiv:1503.08716Mar 30, 20151 citation

Entanglement and Quantum Phase Transition in Quantum Spin Systems

Synge Todo

Jan 1, 20150 citations

Investigation of Quantum Phase Transition and Entanglement in Spin Models

H. Y. Shik

Jan 1, 20110 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

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.