Quantum phase transitions in alternating transverse Ising chains: Rigorous analytical and exact numerical results

TL;DR

This paper investigates quantum phase transitions in alternating transverse Ising chains using exact analytical and numerical methods, revealing multiple transitions depending on system parameters while showing similar critical behavior to uniform chains.

Contribution

It provides rigorous analytical and exact numerical analysis of quantum phase transitions in alternating transverse Ising chains, highlighting the dependence on system parameters.

Findings

Multiple quantum phase transitions depend on parameters

Critical behavior matches that of uniform chains

Numerical results extend up to 900 spins

Abstract

We examine the ground state properties of the s=1/2 transverse Ising chain with regularly alternating bonds and fields using exact analytical results and exact numerical data for long (up to N=900) and short (N=20) chains. For a given period of alternation the system may exhibit a series of quantum phase transitions, where the number of transitions depends on the concrete set of the parameters of the Hamiltonian. The critical behaviour for the nonuniform and the uniform chain is the same.