Phase transitions and generalized biorthogonal polarization in non-Hermitian systems
Elisabet Edvardsson,
Flore Kunst,
Tsuneya Yoshida,
Emil J. Bergholtz
Physical Review Research
2
(4)
043046
(2020)
| Journal
| PDF
Phase transitions and generalized biorthogonal polarization in non-Hermitian systems
Elisabet Edvardsson,
Flore Kunst,
Tsuneya Yoshida,
Emil J. Bergholtz
Physical Review Research
2
(4)
043046
(2020)
| Journal
Non-Hermitian (NH) Hamiltonians can be used to describe dissipative systems, notably including systems with gain and loss, and are currently intensively studied in the context of topology. A salient difference between Hermitian and NH models is the breakdown of the conventional bulk-boundary correspondence, invalidating the use of topological invariants computed from the Bloch bands to characterize boundary modes in generic NH systems. One way to overcome this difficulty is to use the framework of biorthogonal quantum mechanics to define a biorthogonal polarization, which functions as a real-space invariant signaling the presence of boundary states. Here, we generalize the concept of the biorthogonal polarization beyond the previous results to systems with any number of boundary modes and show that it is invariant under basis transformations as well as local unitary transformations. Additionally, we focus on the anisotropic Su-Schrieffer-Heeger chain and study gap closings analytically. We also propose a generalization of a previously developed method with which to find all the bulk states of the system with open boundaries to NH models. Using the exact solutions for the bulk and boundary states, we elucidate genuinely NH aspects of the interplay between the bulk and boundary at the phase transitions.
Dissipative analog of four-dimensional quantum Hall physics
Fanny Terrier,
Flore Kunst
Physical Review Research
2
(2)
023364
(2020)
| Journal
| PDF
Dissipative analog of four-dimensional quantum Hall physics
Fanny Terrier,
Flore Kunst
Physical Review Research
2
(2)
023364
(2020)
| Journal
Four-dimensional quantum Hall (QH) models usually rely on synthetic dimensions for their simulation in experiment. Here, we study a QH system which features a nontrivial configuration of three-dimensional Weyl cones on its boundaries. We propose a three-dimensional analog of this model in the form of a dissipative Weyl semimetal (WSM) described by a non-Hermitian (NH) Hamiltonian, which in the long-time limit manifests the anomalous boundary physics of the four-dimensional QH model in the bulk spectrum. The topology of the NH WSM is captured by a three-dimensional winding number whose value is directly related to the total chirality of the surviving Weyl nodes. Upon taking open boundary conditions, instead of Fermi arcs, we find exceptional points with an order that scales with system size.
Contact
Lise Meitner Research Group Flore Kunst
Max Planck Institute for the Science of Light Staudtstr. 2 91058 Erlangen, Germany
