REVIEW 12 cited by
Symmetry and Topology in Non-Hermitian Physics
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
We develop a complete theory of symmetry and topology in non-Hermitian physics. We demonstrate that non-Hermiticity ramifies the celebrated Altland-Zirnbauer symmetry classification for insulators and superconductors. In particular, charge conjugation is defined in terms of transposition rather than complex conjugation due to the lack of Hermiticity, and hence chiral symmetry becomes distinct from sublattice symmetry. It is also shown that non-Hermiticity enables a Hermitian-conjugate counterpart of the Altland-Zirnbauer symmetry. Taking into account sublattice symmetry or pseudo-Hermiticity as an additional symmetry, the total number of symmetry classes is 38 instead of 10, which describe intrinsic non-Hermitian topological phases as well as non-Hermitian random matrices. Furthermore, due to the complex nature of energy spectra, non-Hermitian systems feature two different types of complex-energy gaps, point-like and line-like vacant regions. On the basis of these concepts and K-theory, we complete classification of non-Hermitian topological phases in arbitrary dimensions and symmetry classes. Remarkably, non-Hermitian topology depends on the type of complex-energy gaps and multiple topological structures appear for each symmetry class and each spatial dimension, which are also illustrated in detail with concrete examples. Moreover, the bulk-boundary correspondence in non-Hermitian systems is elucidated within our framework, and symmetries preventing the non-Hermitian skin effect are identified. Our classification not only categorizes recently observed lasing and transport topological phenomena, but also predicts a new type of symmetry-protected topological lasers with lasing helical edge states and dissipative topological superconductors with nonorthogonal Majorana edge states. Furthermore, our theory provides topological classification of Hermitian and non-Hermitian free bosons.
Forward citations
Cited by 12 Pith papers
-
Non-Hermitian Quantum Adiabatic Algorithm
A history-decoupled Hamiltonian mapping makes non-Hermitian adiabatic quantum optimization pseudospectrally stable, achieving polynomial-time (per configuration) evolution on the CK maximum-independent-set benchmarks.
-
A real-space exceptional ring mediates an eigenframe-charge transition in a non-Hermitian skyrmion
Non-Hermitian skyrmions split their topological charge into a protected real charge and a complex charge that loses quantization and breaks at exceptional points.
-
Pseudospectral phenomena and the origin of the non-Hermitian skin effect
The non-Hermitian skin effect originates from spectral instability and non-reciprocity instead of point-gap winding of the Bloch Hamiltonian.
-
Non-Hermitian Structure and Exceptional Points in Yang-Mills Theory from Analytic Continuation of Nc
Analytic continuation of Nc in Yang-Mills theory produces non-Hermitian operator spectra with exceptional points, PT-phase transitions, and topological monodromy.
-
Crystalline Spectral Form Factors
Strong level repulsion produces damped crystalline oscillations of the spectral form factor, with a Debye-Waller suppression, a new plateau time scale t* ≈ t_H sqrt(β/4), and predictable derivative singularities.
-
Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models
Non-Hermitian free-fermion entanglement spectra can be computed efficiently, and the biorthogonal entanglement Hamiltonian reproduces bulk topology in line-gapped phases.
-
Generalized bulk-edge correspondence for non-hermitian topological systems
A modified periodic boundary condition with a decay parameter b makes the bulk-edge correspondence work for a non-Hermitian SSH model in an enlarged parameter space.
-
Nonhermitian defect states from lifetime differences
Nonhermitian defect states form at an interface in a coupled-resonator chain when the mode pair's lifetimes split but their frequencies stay aligned, as realized by nanoparticle perturbations on symmetric microresonators.
-
Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
Bulk wave-packet dynamics, through the drift-velocity dependence of the Lyapunov exponent, can reveal the non-Hermitian skin effect and non-Bloch symmetry-breaking transitions.
-
Non-Hermitian Floquet topological phases in the double-kicked rotor
The non-Hermitian double kicked rotor hosts Floquet topological phases labeled by two winding numbers, detectable by a generalized mean chiral displacement, with edge states counted by the bulk invariants.
-
Hidden Chern number in one-dimensional non-Hermitian chiral-symmetric systems
The topology of certain one-dimensional non-Hermitian chains is captured by a Chern number of an effective two-dimensional Hermitian Hamiltonian, and this hidden Chern number predicts zero-real-energy end states.
-
Perspective on topological states of non-Hermitian lattices
A perspective review that attributes defectiveness in non-Hermitian lattices to boundary conditions of a hypothetical Hermitian parent system.
Discussion (0). Continue with ORCID to comment.