Entanglement Spectrum, Critical Exponents and Order Parameters in Quantum Spin Chains

TL;DR

This paper demonstrates that the Schmidt gap in the entanglement spectrum of finite quantum spin chains acts as a local order parameter, signaling quantum critical points and scaling with universal critical exponents.

Contribution

It establishes the Schmidt gap as a universal, measurable indicator of quantum phase transitions in spin chains, linking entanglement properties to critical phenomena.

Findings

Schmidt gap signals quantum critical points.

Schmidt gap scales with universal critical exponents.

Identifies Schmidt gap as a local order parameter.

Abstract

We investigate the entanglement spectrum near criticality in finite quantum spin chains. Using finite size scaling we show that when approaching a quantum phase transition, the Schmidt gap, i.e., the difference between the two largest eigenvalues of the reduced density matrix, signals the critical point and scales with universal critical exponents related to the relevant operators of the corresponding perturbed conformal field theory describing the critical point. Such scaling behavior allows us to identify explicitly the Schmidt gap as a local order parameter.