Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition

By L. Herviou, J. Bardarson, N. Regnault. Physical Review A, 2019

157 citations recorded by the source corpus.

We address the breakdown of the bulk-boundary correspondence observed in non-Hermitian systems, where open and periodic systems can have distinct phase diagrams. The correspondence can be completely restored by considering the Hamiltonian's singular-value decomposition instead of its eigendecomposition. This leads to a natural topological description in terms of a flattened singular decomposition. This description is equivalent to the usual approach for Hermitian systems and coincides with a recent proposal for the classification of non-Hermitian systems. We generalize the notion of the entanglement spectrum to non-Hermitian systems, and show that the edge physics is indeed completely captured by the periodic bulk Hamiltonian. We exemplify our approach by considering the chiral non-Hermitian Su-Schrieffer-Heger and Chern insulator models. Our work advocates a different perspective on topological non-Hermitian Hamiltonians, paving the way to a better understanding of their entanglement structure.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8b28eb0b4713fbf6b0059e1bae8afcd434b2fa5e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. K. Kawabata
2. Tokiro Numasawa
3. S. Ryu
4. T. Takayanagi
5. R. Myers
6. Masatoshi Sato
7. V. Hubeny
8. M. Rangamani

In Geometry and Topology

1. K. Kawabata
2. S. Ryu
3. Tokiro Numasawa
4. T. Takayanagi
5. R. Myers
6. V. Hubeny
7. M. Rangamani
8. M. Headrick

Citations in the corpus

• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect (2022, methodology): “Here, we calculate the entanglement entropy from a single wave function instead of the biorthogonal density operator constructed from both right and left eigenstates [86, 88, 90].”
• Higher-order non-Hermitian skin effect (2020, unknown): “[63] L.”
• Exceptional topology of non-Hermitian systems (2019, unknown): “For a sufficiently small gap (or short Hermitian domain), the skin states can tunnel through, and behavior similar to the NH model with PBC is retrieved (Kunst et al. , 2018; Herviou, Bardarson, and Regnault, 2019).”