PHASE TRANSITIONS IN QUANTUM SPIN CHAINS

Ming Zhong, Xiaoxian Liu, Peiqing Tong

The quantum phase transitions of four kinds of nonuniform anisotropic XY quantum spin chains in a transverse field are studied by the Lee-Yang zeros method. It is found that the closed curves of the partition function zeros cut the positive real axis at the quantum phase transition points. The results are checked by the explicit calculations of the magnetization.

A. Zheludev

Oleg Derzhko

This chapter is devoted to a discussion of quantum phase transitions in regularly alternating spin-1/2 Ising chain in a transverse field. After recalling some generally-known topics of the classical (temperature-driven) phase transition theory and some basic concepts of the quantum phase transition theory I pass to the statistical mechanics calculations for a one-dimensional spin-1/2 Ising model in a transverse field, which is the simplest possible system exhibiting the continuous quantum phase transition. The essential tool for these calculations is the Jordan-Wigner fermionization. The latter technique being completed by the continued fraction approach permits to obtain analytically the thermodynamic quantities for a `slightly complicated' model in which the intersite exchange interactions and on-site fields vary regularly along a chain. Rigorous analytical results for the ground-state and thermodynamic quantities, as well as exact numerical data for the spin correlations computed for long chains (up to a few thousand sites) demonstrate how the regularly alternating bonds/fields effect the quantum phase transition. I discuss in detail the case of period 2, swiftly sketch the case of period 3 and finally summarize emphasizing the effects of periodically modulated Hamiltonian parameters on quantum phase transitions in the transverse Ising chain and in some related models.

R. Micnas, K. A. Chao

C. Degli, Esposti Boschi

Yanchao Li, Wing Chi Yu, Hai‐Qing Lin