Related papers: Braid Group and Topological Phase Transitions in N…
We demonstrate that periodically driven quantum rotors provide a promising and broadly applicable platform to implement multi-gap topological phases, where groups of bands can acquire topological invariants due to non-Abelian braiding of…
The complex eigenenergies and non-orthogonal eigenstates of non-Hermitian systems exhibit unique topological phenomena that cannot appear in Hermitian systems. Representative examples are the non-Hermitian skin effect and exceptional…
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 symmetry breaking phase transitions in…
The non-Bloch topology leads to the emergence of various counter-intuitive phenomena in non-Hermitian systems under the open boundary condition (OBC), which can not find a counterpart in Hermitian systems. However, in the non-Hermitian…
Degeneracy points in non-Hermitian systems are of great interest. While a homotopic framework exists for understanding their behavior in the absence of symmetry, it does not apply to symmetry-protected degeneracy points with reduced…
Non-Hermitian quantum systems can exhibit unique observables characterizing topologically protected transport in the presence of decay. The topological protection arises from winding numbers associated with non-decaying dark states, which…
We establish non-Hermitian topological mechanics in one dimensional (1D) and two dimensional (2D) lattices consisting of mass points connected by meta-beams that lead to odd elasticity. Extended from the "non-Hermitian skin effect" in 1D…
Recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. A particular interest centers on the topological…
By studying the topological invariance andBerry phase in non-Hermitian systems, we reveal the basic properties of the complex Berry phase and generalize the global Berry phases Q to identify the topological invariance for non-Hermitian…
In recent years, non-Hermitian phases in classical and quantum systems have garnered significant attention. In particular, their intriguing band geometry offers a platform for exploring unique topological states and unconventional quantum…
We consider universal statistical properties of systems that are characterized by phase states with macroscopic degeneracy of the ground state. A possible topological order in such systems is described by non-linear discrete equations. We…
Critical edge states appear at the bulk gap closing points of topological transitions. Their emergence signify the existence of topologically nontrivial critical points, whose descriptions fall outside the scope of gapped topological…
The time evolution of a system with a time-dependent non-Hermitian Hamiltonian is in general unstable with exponential growth or decay. A periodic driving field may stabilize the dynamics because the eigenphases of the associated Floquet…
Both theoretical and experimental studies of topological phases in non-Hermitian systems have made a remarkable progress in the last few years of research. In this article, we review the key concepts pertaining to topological phases in…
Nodal lines inside the momentum space of three-dimensional crystalline solids are topologically stabilized by a $\pi$-flux of Berry phase. Nodal-line rings in $\mathcal{PT}$-symmetric systems with negligible spin-orbit coupling (here…
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 topologically protected boundary modes,…
We propose and present a concept of Topological Distance (TD), obtained from the integration of trace distance over the generalized Brillouin zone, in order to characterize the topological transitions of non-Hermitian systems. Specifically,…
Topological phases of matter are classified based on their Hermitian Hamiltonians, whose real-valued dispersions together with orthogonal eigenstates form nontrivial topology. In the recently discovered higher-order topological insulators…
We study topological properties of one-dimensional non-Hermitian systems without chiral symmetry and give phase diagrams characterized by topological invariants $\nu_E$ and $\nu_{total}$, associated with complex energy vorticity and…
Topological phases of matter lie at the heart of physics, connecting elegant mathematical principles to real materials that are believed to shape future electronic and quantum computing technologies. To date, studies in this discipline have…