Entanglement and local extremes at an infinite-order quantum phase transition

TL;DR

This paper investigates how entanglement measures can characterize infinite-order quantum phase transitions in spin chains, revealing limitations of pairwise entanglement and the utility of block entanglement in identifying phase diagrams.

Contribution

It compares entanglement behavior in Ashkin-Teller and XXZ models, showing that block entanglement can identify phase transitions where pairwise entanglement fails.

Findings

Pairwise entanglement fails to characterize the infinite-order QPT in Ashkin-Teller.

Block entanglement entropy can identify the quantum phase diagram.

Local extrema of entanglement may occur without phase transitions.

Abstract

The characterization of an infinite-order quantum phase transition (QPT) by entanglement measures is analyzed. To this aim, we consider two closely related solvable spin-1/2 chains, namely, the Ashkin-Teller and the staggered XXZ models. These systems display a distinct pattern of eigenstates but exhibit the same thermodynamics, i.e. the same energy spectrum. By performing exact diagonalization, we investigate the behavior of pairwise and block entanglement in the ground state of both models. In contrast with the XXZ chain, we show that pairwise entanglement fails in the characterization of the infinite-order QPT in the Ashkin-Teller model, although it can be achieved by analyzing the distance of the pair state from the separability boundary. Concerning block entanglement, we show that both XXZ and Ashkin-Teller models exhibit identical von Neumann entropies as long as a suitable choice of blocks is performed. Entanglement entropy is then shown to be able to identify the quantum phase diagram, even though its local extremes (either maximum or minimum) may also appear in the absence of any infinite-order QPT.