A renormalization group approach to non-Hermitian topological quantum criticality

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.

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Cited by in corpus (8)

• Topological Non-Hermitian skin effect
• Nonlinear non-Hermitian skin effect
• Real Non-Hermitian Energy Spectra Without Any Symmetry
• Two-dimensional anisotropic non-Hermitian Lieb lattice
• Effective impurity behavior emergent from non-Hermitian proximity effect
• Non-Hermitian quantum gases: a platform for imaginary time crystals
• Quasi-stationary solutions in non-Hermitian systems
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains