A renormalization group approach to non-Hermitian topological quantum criticality

TL;DR

This paper introduces a real-space renormalization group method tailored for non-Hermitian topological quantum systems, effectively identifying critical points and overcoming limitations of traditional momentum-space approaches.

Contribution

It proposes a novel real-space decimation scheme for non-Hermitian systems that accurately captures criticality and simplifies the analysis of complex models.

Findings

The scheme preserves critical points as fixed points under RG.

It overcomes the limitations of standard momentum-space RG in non-Hermitian systems.

The method facilitates the search for critical points in complicated models.

Abstract

Critical transition points between symmetry-broken phases are characterized as fixed points in the renormalization group (RG) theory. We show that, following the standard Wilsonian procedure that traces out the large momentum modes, this well known fact can break down in non-Hermitian systems. Based on non-Hermitian Su-Schrieffer-Hegger (SSH)-type models, we propose a real-space decimation scheme to study the criticality between the topological and trivial phase. We provide concrete examples and an analytic proof to show that the real-space scheme perfectly overcomes the insufficiency of the standard method, especially in the sense that it always preserves the system at criticality as fixed points under RG. The proposed method can also greatly simplify the search of critical points for complicated non-Hermitian models by ruling out the irrelevant operators. These results pave the way towards more advanced RG-based techniques for the interacting non-Hermitian quantum systems.