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

Abstract

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 ρ of the spin pair from the ground state |Ψ⟩ of a spin chain, and then identify the quantum correlation part ${\rho }_q$ embedded in ρ. If the spin chain is translationally symmetric and characterized by a nearest-neighbor two-body spin interaction, we can determine uniquely the form of ${\rho }_q$ as $W|\mathrm{\Phi }\rangle \langle \mathrm{\Phi }|$ with the weight $W$ $\le 1$, and quantify the fluctuation properties using the two-spin entangled state $|\mathrm{\Phi }\rangle$. We demonstrate the framework for a transverse-field quantum Ising spin chain and indicate its validity for more general spin chain models.