Exact formulas of the end-to-end Green's functions in non-Hermitian systems

Abstract

Green's function in non-Hermitian systems has recently been revealed to be capable of directional amplification in some cases. The exact formulas for end-to-end Green's functions are significantly important for studies of both non-Hermitian systems and their applications. In this work, based on the Widom's formula, we derive exact formulas for the end-to-end Green's functions of single-band systems which depend on the roots of a simple algebraic equation. These exact formulas allow direct and accurate comparisons between theoretical results and experimentally measured quantities. In addition, we verify the prior established integral formula in the bulk region to agree with the result in our framework. We also find that the speed at which the Green's functions in the bulk region approach the prior established integral formula is not slower than an exponential decay as the system size increases. The correspondence between the signal amplification and the non-Hermitian skin effect is confirmed.

arXiv comment13 pages, 5 figures

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• Dynamic skin effects in non-Hermitian systems
• Anatomy of open-boundary bulk in multiband non-Hermitian systems
• Degeneracy and defectiveness in non-Hermitian systems with open boundary
• Topological superconductivity enhanced by exceptional points
• Constraints of internal symmetry on the non-Hermitian skin effect and bidirectional skin effect under the action of the Hermitian conjugate of time-reversal symmetry
• General theory for infernal points in non-Hermitian systems
• Formal Green's function theory in non-Hermitian lattice systems
• 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
• Beyond characteristic equations: A unified one-dimensional non-Bloch band theory via wavefunction data
• Topology of the generalized Brillouin zone of one-dimensional models