Quantum Phase Transitions in Spin-1/2 Ising Chain in Regularly Alternating Transverse Field: Spin Correlation Functions

TL;DR

This paper investigates how regular alternation in a spin-1/2 Ising chain's transverse field influences quantum phase transitions, revealing up to two transition points and two types of critical behavior through numerical analysis.

Contribution

It demonstrates the dependence of quantum phase transition points on Hamiltonian parameters and identifies two universality classes of critical behavior in the model.

Findings

Number of quantum phase transitions can reach up to 2p for period p.

Two types of critical behavior are observed: Ising universality and weaker singularities.

Numerical calculations were performed on chains of up to 5400 sites.

Abstract

We consider the spin-1/2 Ising chain in a regularly alternating transverse field to examine the effects of regular alternation on the quantum phase transition inherent in the quantum Ising chain. The number of quantum phase transition points strongly depends on the specific set of the Hamiltonian parameters but never exceeds 2p where p is the period of alternation. Calculating the spin correlation functions numerically (for long chains of up to 5400 sites) and determining the critical exponents we have demonstrated that two types of critical behavior are possible. In most cases the square-lattice Ising model universality class occurs, however, a weaker singularity may also take place.