Non-Hermitian bulk–boundary correspondence in quantum dynamics

  title={Non-Hermitian bulk–boundary correspondence in quantum dynamics},
  author={Lei Xiao and Tianshu Deng and Kunkun Wang and Gaoyan Zhu and Zhong Wang and Wei Yi and Peng Xue},
  journal={Nature Physics},
Bulk–boundary correspondence, a guiding principle in topological matter, relates robust edge states to bulk topological invariants. Its validity, however, has so far been established only in closed systems. Recent theoretical studies indicate that this principle requires fundamental revisions for a wide range of open systems with effective non-Hermitian Hamiltonians. Therein, the intriguing localization of nominal bulk states at boundaries, known as the non-Hermitian skin effect, suggests a non… 
Non-Hermitian bulk-boundary correspondence in a periodically driven system
Bulk-boundary correspondence, connecting the bulk topology and the edge states, is an essential principle of the topological phases. However, the bulk-boundary correspondence is broken down in
Point-gap topology with complete bulk-boundary correspondence in dissipative quantum systems
The spectral and dynamical properties of dissipative quantum systems, as modeled by a damped oscillator in the Fock space, are investigated from a topological point of view. Unlike a physical lattice
Point-gap topology with complete bulk-boundary correspondence and anomalous amplification in the Fock space of dissipative quantum systems
The spectral and dynamical properties of dissipative quantum systems, as modeled by a damped oscillator in the Fock space, are investigated from a topological point of view. Unlike a physical lattice
State-Dependent Topological Invariants and Anomalous Bulk-Boundary Correspondence in Non-Hermitian Topological Systems with Generalized Inversion Symmetry
The breakdown of the bulk-boundary correspondence in non-Hermitian (NH) topological systems is an open, controversial issue. In this paper, to resolve this issue, we ask the following question: Can a
Selective and tunable excitation of topological non-Hermitian quasi-edge modes
  • S. Longhi
  • Mathematics
    Proceedings of the Royal Society A
  • 2022
Non-Hermitian lattices under semi-infinite boundary conditions sustain an extensive number of exponentially localized states, dubbed non-Hermitian quasi-edge modes. Quasi-edge states arise rather
Exponentially growing bulk Green functions as signature of nontrivial non-Hermitian winding number in one dimension
A nonzero non-Hermitian winding number indicates that a gapped system is in a nontrivial topological class due to the non-Hermiticity of its Hamiltonian. While for Hermitian systems nontrivial
Bulk-Boundary Correspondence for Non-Hermitian Hamiltonians via Green Functions.
It is found that the non-Hermitian winding number in one dimension signals a topological phase transition in the bulk: It implies spatial growth of the bulk Green function.
Hybrid skin-topological modes without asymmetric couplings
Non-Hermitian skin effect (NHSE) in non-Hermitian lattice systems, associated with a point gap on the complex energy plane, has attracted great theoretical and experimental interest. Much less is
Unraveling non-Hermitian pumping: Emergent spectral singularities and anomalous responses
Within the expanding field of non-Hermitian physics, non-Hermitian pumping has emerged as a key phenomenon, epitomized through the skin effect via extensive boundary mode accumulation modifying the
Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
We investigate the roles of non-Hermitian topology in spectral properties and entanglement structures of open systems. In terms of spectral theory, we give a unified understanding of two


Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems.
This work provides a comprehensive framework for generalized bulk-boundary correspondence and a quantized biorthogonal polarization that is formulated directly in systems with open boundaries, including exactly solvable non-Hermitian extensions of the Su-Schrieffer-Heeger model and Chern insulators.
Edge States and Topological Invariants of Non-Hermitian Systems.
This work obtains the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by theNon-Bloch winding number instead of the Bloch-Hamiltonian-based topological number.
New topological invariants in non-Hermitian systems.
  • Ananya Ghatak, T. Das
  • Physics, Mathematics
    Journal of physics. Condensed matter : an Institute of Physics journal
  • 2019
This article reviews the key concepts pertaining to topological phases in non-Hermitian Hamiltonians with relevant examples and realistic model setups, and highlights potential applications of some of these unique topological features of the non- hermitianHamiltonians.
Topological Phases of Non-Hermitian Systems
Recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. A particular
Anatomy of skin modes and topology in non-Hermitian systems
A non-Hermitian system can exhibit extensive sensitivity of its complex energy spectrum to the imposed boundary conditions, which is beyond any known phenomenon from Hermitian systems. In addition to
Non-Hermitian Chern Bands.
This work introduces non-Bloch Chern numbers that faithfully predict the numbers of chiral edge modes and highlights a unique feature of non-Hermitian bands and suggests a non- Bloch framework to characterize their topology.
Probing non-Hermitian skin effect and non-Bloch phase transitions
In non-Hermitian crystals showing the non-Hermitian skin effect, ordinary Bloch band theory and Bloch topological invariants fail to correctly predict energy spectra, topological boundary states, and
Non-Hermitian Boundary Modes and Topology.
This work exposes a direct relation between the presence of a point gap invariant and the appearance of skin modes when this gap is trivialized by an edge, and can expose novel non-Hermitian topological regimes beyond the reach of previous methods.
Non-Bloch topological invariants in a non-Hermitian domain wall system
We study non-Bloch bulk-boundary correspondence in a non-Hermitian Su-Schieffer-Heeger model in a domain-wall configuration where the left and right bulks have different parameters. Focusing on the
Non-Hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points
Capital to topological insulators, the bulk-boundary correspondence ties a topological invariant computed from the bulk (extended) states with those at the boundary, which are hence robust to