2020/05/20 by Boran Zhou, Rui Wang, Baigeng Wang
Mathematics · Physics and Astronomy · #Combinatorics #Criticality #Fixed point #Hermitian matrix #Mathematical analysis #Mathematical physics #Mathematics #Physics #Position and momentum space #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Renormalization #Renormalization group #Theoretical physics #Topological Materials and Phenomena #Topology (electrical circuits) #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.102.205116
published as Phys. Rev. B 102, 205116 (2020)
arxiv created 2020/05/20 · openalex publication_date 2020/11/13 · arxiv updated 2020/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Critical transition points between symmetry-broken phases are usually characterized as fixed points in the renormalization group (RG) theory. We show that, following the standard Wilsonian procedure that iteratively traces out the large-momentum modes, this well-known fact can easily break down in non-Hermitian systems under open boundary conditions. Based on non-Hermitian Su-Schrieffer-Heeger-type models, we propose a RG scheme based on real-space decimation. We provide concrete examples and an analytic proof to show that the real-space scheme always respects the critical points under RG transformations. We investigate the correlation length of order parameters in the vicinity of critical points. Its divergence and scaling behavior remain intact under the real-space decimation, indicating that our method can be successfully applied to study the critical phenomena in non-Hermitian systems. These results suggest that the real-space RG method will find versatile applications in interacting non-Hermitian quantum systems.