The partition function zeros of the anisotropic $XY$ chain in a complex transverse field are studied analytically and numerically. It is found that the partition function zeros of the periodic and quasiperiodic quantum Ising chain lie on the circle at zero temperature and the radius equal to the values of the critical field. For the periodic and quasiperiodic anisotropic $XY$ chains, the closed curves are split to two or three closed curves as the anisotropic parameter $\gamma$ decreases at a given ratio of two kinds of exchange interactions. For the isotropic $XX$ case, the partition function zeros lie on the straight segments which are parallel to the real axis and the segments move towards the real axis as the temperature goes to zero.

• Received 10 January 2006

DOI:https://doi.org/10.1103/PhysRevLett.97.017201