Matrix Product States and Quantum Phase Transitions

TL;DR

This paper introduces a matrix product state method to analyze quantum phase transitions, successfully applying it to the XXZ spin chain and identifying solvable parameter regions.

Contribution

The paper presents a novel matrix product state approach for studying quantum phase transitions, providing analytical insights and comparison with numerical results.

Findings

Analytical analysis of the XXZ spin-one chain confirms the method's effectiveness.

Identification of parameter regions likely to be exactly solvable.

Comparison shows favorable agreement with previous numerical studies.

Abstract

We have developed a new approach based on matrix product representations of ground states to study Quantum Phase Transitions (QPT). As confirmation of the power of our approach we have analytically analyzed the XXZ spin-one chain with uniaxial single-ion-type anisotropy and our results compare favourably with previous numerical studies. In addition, our description lets to know which part of parameters space of the Hamiltonian is most likely to be exactly solvable.