Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension

TL;DR

This paper investigates the quantum entanglement properties of fermionic symmetry-enriched quantum critical points in one dimension, revealing topologically distinct phases and transitions, and generalizing bulk-boundary correspondence to critical systems.

Contribution

It constructs exactly solvable models based on stacked Kitaev chains to analyze topological phases and transitions at fermionic critical points, uncovering new topological degeneracies and a Lifshitz multicritical point.

Findings

Identified three topologically distinct gapped phases with different winding numbers.

Discovered two transition lines with fundamentally different topological properties.

Found a Lifshitz multicritical point with nontrivial topological degeneracy.

Abstract

Quantum entanglement can be an effective diagnostic tool for probing topological phases protected by global symmetries. Recently, the notion of nontrivial topology in critical systems has been proposed and is attracting growing attention. In this work, as a concrete example, we explore the quantum entanglement properties of fermionic symmetry-enriched quantum critical points by constructing exactly solvable models based on stacked multiple Kitaev chains. We first analytically establish the global phase diagram using entanglement entropy and reveal three topologically distinct gapped phases with different winding numbers, along with three topologically distinct transition lines separating them. Importantly, we unambiguously demonstrate that two transition lines exhibit fundamentally different topological properties despite sharing the same central charge. Specifically, they display nontrivial topological degeneracy in the entanglement spectrum under periodic boundary conditions, thereby generalizing the Li-Haldane bulk-boundary correspondence to a broader class of fermionic symmetry-enriched criticality. Additionally, we identify a novel Lifshitz multicritical point at the intersection of the three transition lines, which also exhibits nontrivial topological degeneracy. This work provides a valuable reference for investigating gapless topological phases of matter from the perspective of quantum entanglement.