Fermionic quantum criticality through the lens of topological holography

TL;DR

This paper applies topological holography to analyze fermionic quantum critical points and gapless phases, revealing new exotic phases and symmetry properties in one-dimensional fermionic systems.

Contribution

It extends the topological holographic framework to $(1+1)d$ fermionic systems, connecting spin structures with SymTFT and classifying fermionic phases and transitions.

Findings

Identification of fermionic gapped phases and phase transitions.

Discovery of exotic fermionic quantum critical points.

Characterization of fermionic gapless SPT and SSB phases.

Abstract

We utilize the topological holographic framework to characterize and gain insights into the nature of quantum critical points and gapless phases in fermionic quantum systems. Topological holography is a general framework that describes the generalized global symmetry and the symmetry charges of a local quantum system in terms of a slab of a topological order, termed as the symmetry topological field theory (SymTFT), in one higher dimension. In this work, we consider a generalization of the topological holographic picture for $(1+1)d$ fermionic quantum phases of matter. We discuss how spin structures are encoded in the SymTFT and establish the connection between the formal fermionization formula in quantum field theory and the choice of fermionic gapped boundary conditions of the SymTFT. We demonstrate the identification and the characterization of the fermionic gapped phases and phase transitions through detailed analysis of various examples, including the fermionic systems with $\mathbb{Z}_{2}^{F}$, $\mathbb{Z}_{2} \times \mathbb{Z}_{2}^{F}$, $\mathbb{Z}_{4}^{F}$, and the fermionic version of the non-invertible $\text{Rep}(S_{3})$ symmetry. Our work uncovers many exotic fermionic quantum critical points and gapless phases, including two kinds of fermionic symmetry enriched quantum critical points, a fermionic gapless symmetry protected topological (SPT) phase, and a fermionic gapless spontaneous symmetry breaking (SSB) phase that breaks the fermionic non-invertible symmetry.