Quantum phase transitions of periodic anisotropic XY chain in a transversefield

The transfer matrix method is used to study the quantum phase transitions o f the uniform and periodic anisotropic, XY quantum spin in a transverse fie ld, which is defined by H = -1/2 Sigma (n) [J(n)(sigma (x)(n)sigma (x)(n+1) + alpha sigma (y)(n)sigma (y)(n-1)) + h sigma (z)(n)]. In zero temperature . it is found that the quantum phase transition point corresponds to h/J I for uniform chain (J(n) = J). For periodic chain, there is more than one ph ase transition point at some parameter region. In case the couplings take t wo alternating values, with ratio the number of phase transition points are dependent on the parameters (alpha and gamma) and the structure of the sys tems. These are different from that of quantum Ising chain in a transverse field. The critical points and the conditions of their existence are obtain ed analytically for period-two and three chains. The results are in good ag reement with numerical results. The reasons of quantum phase transitions ar e discussed. (C) 2001 Elsevier Science B.V. All rights reserved.