Related papers: Evidence for Exceptional Points as Topological Def…
The behavior of quantum states at exceptional points and at critical points associated with quantum phase transitions is intriguing yet puzzling. In this study, we present an alternative method for obtaining the Berry potentials using the…
Studies have shown that the Hilbert spaces of non-Hermitian systems require nontrivial metrics. Here, we demonstrate how evolution dimensions, in addition to time, can emerge naturally from a geometric formalism. Specifically, in this…
We study the quantum evolution of a non-Hermitian qubit realized as a submanifold of a dissipative superconducting transmon circuit. Real-time tuning of the system parameters to encircle an exceptional point results in non-reciprocal…
This article is an expository account aimed at viewing entanglement in finite-dimensional quantum many-body systems as a phenomenon of global geometry. While the mathematics of general quantum states has been studied extensively, this…
An exceptional point is a special point in parameter space at which two (or more) eigenvalues and eigenvectors coincide. The discovery of exceptional points within mechanical and optical systems has uncovered peculiar effects in their…
The correspondence between exotic quantum holonomy that occurs in families of Hermitian cycles, and exceptional points (EPs) for non-Hermitian quantum theory is examined in quantum kicked tops. Under a suitable condition, an explicit…
This work introduces a new class of robust states known as Exceptional Boundary (EB) states, which are distinct from the well-known topological and non-Hermitian skin boundary states. EB states occur in the presence of exceptional points,…
Non-Hermitian systems can produce branch singularities known as exceptional points (EPs). Different from singularities in Hermitian systems, the topological properties of an EP can involve either the winding of eigenvalues that produces a…
The existence of bound states in quantum mechanics with no classical counterpart has been a subject of interest for a long time. Cross-wires and cavities connected to infinite leads are typical examples in which open geometries with bulges…
Non-Hermitian systems distinguish themselves from Hermitian systems by exhibiting a phase transition point called an exceptional point (EP), which is the point at which two eigenstates coalesce under a system parameter variation. Many…
Exceptional points (EPs) are non-Hermitian degeneracies where eigenvalues and eigenvectors coalesce, giving rise to unusual physical effects across scientific disciplines. The concept of EPs has recently been extended to nonlinear physical…
We show that certain global anomalies can be detected in an elementary fashion by analyzing the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory. Distinct anomalous behaviours imprinted in the Hilbert…
Exceptional points are interesting physical phenomena in non-Hermitian physics at which the eigenvalues are degenerate and the eigenvectors coalesce. In this paper, we find that the universal feature of arbitrary non-Hermitian two level…
Owing to the presence of exceptional points (EPs), non-Hermitian (NH) systems can display intriguing topological phenomena without Hermitian analogs. However, experimental characterizations of exceptional topological invariants have been…
We investigate the emergence and corresponding nature of exceptional points located on exceptional hyper-surfaces of non-hermitian transfer matrices for finite-range one-dimensional lattice models. We unravel the non-trivial role of these…
Phase transitions in open quantum systems, which are associated with the formation of collective states of a large width and of trapped states with rather small widths, are related to exceptional points of the Hamiltonian. Exceptional…
Band structures of metamaterials described by a nonlinear eigenvalue problem are beyond the existing topological band theory. In this paper, we analyze non-Hermitian topology under the nonlinearity of eigenvalues. Specifically, we elucidate…
An adiabatic change of a bound state along a closed circuit in the parameter space can induces holonomies not only in the phase of the state, but also in the associated eigenspace and eigenvalue. The former is the well-known Berry phase…
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is…
We study the evolution of quantum eigenstates in the presence of level crossing under adiabatic cyclic change of environmental parameters. We find that exotic holonomies, indicated by exchange of the eigenstates after a single cyclic…