Green's functions of multiband non-Hermitian systems

Abstract

Green's functions of non-Hermitian systems play a fundamental role in various dynamical processes. Because non-Hermitian systems are sensitive to boundary conditions due to the non-Hermitian skin effect, open-boundary Green's functions are closely related to the non-Bloch band theory. While the exact formula of open-boundary Green's functions in single-band non-Hermitian systems proves to be an integral along the generalized Brillouin zone (GBZ), the proper generalization in generic multiband systems remains unclear. In this work, we derive a formula of open-boundary Green's functions in multiband non-Hermitian systems by viewing the multiband GBZ on the Riemann surface. This formula can be applied to describe directional amplification in multiband systems, which can be verified at various experimental platforms.

arXiv comment8 pages, 4 figures

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• Geometric Origin of Non-Bloch PT Symmetry Breaking
• Non-Bloch band theory for non-Hermitian continuum systems
• Steady-state edge burst: From free-particle systems to interaction-induced phenomena
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Abnormal Frequency Response Determined by Saddle Points in Non-Hermitian Crystal Systems
• Formal Green's function theory in non-Hermitian lattice systems
• One-dimensional non-Hermitian band structures as Riemann surfaces
• Real-time edge dynamics of non-Hermitian lattices
• Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory
• Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems
• Topology of the generalized Brillouin zone of one-dimensional models
• Winding-control mechanism of non-Hermitian systems