The anisotropic XY model on the inhomogeneous periodic chain

Abstract

The static and dynamic properties of the anisotropic XY-model $(s=1/2)$ on the inhomogeneous periodic chain, composed of $N$ cells with $n$ different exchange interactions and magnetic moments, in a transverse field $h,$ are determined exactly at arbitrary temperatures. The properties are obtained by introducing the Jordan-Wigner fermionization and by reducing the problem to a diagonalization of a finite matrix of $nth$ order. The quantum transitions are determined exactly by analyzing, as a function of the field, the induced magnetization $1/n{\sum }_{m=1}^n{\mu }_m⟨S_{j,m}^z⟩$ ($j$ denotes the cell, $m$ the site within the cell, ${\mu }_m$ the magnetic moment at site $m$ within the cell) and the spontaneous magnetization $1/n{\sum }_{m=1}^n⟨S_{j,m}^x,⟩$ which is obtained from the correlations $⟨S_{j,m}^x{S}_{j+r,m}^x⟩$ for large spin separations. These results, which are obtained for infinite chains, correspond to an extension of the ones obtained by Tong and Zhong(\textit{Physica B} \textbf{304,}91 (2001)). The dynamic correlations, $⟨S_{j,m}^z(t)S_{j^{\prime },m^{\prime }}^z(0)⟩$, and the dynamic susceptibility, ${\chi }_q^{zz}(\omega ),$ are also obtained at arbitrary temperatures. Explicit results are presented in the limit T=0, where the critical behaviour occurs, for the static susceptibility ${\chi }_q^{zz}(0)$ as a function of the transverse field $h$, and for the frequency dependency of dynamic susceptibility ${\chi }_q^{zz}(\omega )$.

33 pages, 13 figures, 01 table. Revised version (minor corrections) accepted for publiction in Phys. Rev. B

References in corpus (1)

• Divergence of the entanglement range in low dimensional quantum systems

Cited by in corpus (3)

• Ground-state factorization and quantum phase transition in dimerized spin chains
• Geometric phase and quantum phase transition in an inhomogeneous periodic XY spin-1/2 model
• Quantum transitions of the XY model with long-range interactions on the inhomogenous periodic chain