Quantum fidelity and quantum phase transitions in matrix product states

TL;DR

This paper investigates how quantum fidelity can detect phase transitions in matrix product states, revealing singularities and critical behavior despite the ground state energy's analyticity.

Contribution

It demonstrates the effectiveness of the fidelity approach in identifying quantum phase transitions within matrix product states and explores finite size scaling for critical exponents.

Findings

Fidelity successfully detects all present quantum phase transitions.

Finite size scaling of fidelity derivatives helps extract critical exponents.

Singularities in observable expectation values occur despite ground state energy being analytic.

Abstract

Matrix product states, a key ingredient of numerical algorithms widely employed in the simulation of quantum spin chains, provide an intriguing tool for quantum phase transition engineering. At critical values of the control parameters on which their constituent matrices depend, singularities in the expectation values of certain observables can appear, in spite of the analyticity of the ground state energy. For this class of generalized quantum phase transitions we test the validity of the recently introduced fidelity approach, where the overlap modulus of ground states corresponding to slightly different parameters is considered. We discuss several examples, successfully identifying all the present transitions. We also study the finite size scaling of fidelity derivatives, pointing out its relevance in extracting critical exponents.