Observation of arbitrary topological windings of a non-Hermitian band

Wang, Kai; Dutt, Avik; Yang, Ki Youl; Wojcik, Casey C.; Vučković, Jelena; Fan, Shanhui

doi:10.48550/arxiv.2011.14275

Cited by 4 publications

(6 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such results provide important advances to understand the nontrivial interplay between disorder and non-Hermiticity, which is currently a hot area of research [29, 53-61, 64, 67, 69, 71, 73, 74]. The kind of non-Hermitian Hamiltonian with asymmetric hopping amplitudes, considered in this work, could be realized in synthetic matter using, for example, photonic systems [53,64,86,87], topoelectrical circuits [88], mechanical metamaterials [89] or in continuously-measured ultracold atom systems with reservoir engineering [55,90].…”

Section: Discussionmentioning

confidence: 99%

Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper model

Longhi

2019

Phys. Rev. B

150

View full text Add to dashboard Cite

Non-Hermitian extensions of the Anderson and Aubry-André-Harper models are attracting a considerable interest as platforms to study localization phenomena, metal-insulator and topological phase transitions in disordered non-Hermitian systems. Most of available studies, however, resort to numerical results, while few analytical and rigorous results are available owing to the extraordinary complexity of the underlying problem. Here we consider a parity-time (PT ) symmetric extension of the Aubry-André-Harper model, undergoing a topological metal-insulator phase transition, and provide rigorous analytical results of energy spectrum, symmetry breaking phase transition and localization length. In particular, by extending to the non-Hermitian realm the Thouless ′ s result relating localization length and density of states, we derive an analytical form of the localization length in the insulating phase, showing that -like in the Hermitian Aubry-André-Harper modelthe localization length is independent of energy.

show abstract

Section: Discussionmentioning

confidence: 99%

Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper model

Longhi

2019

Phys. Rev. B

150

View full text Add to dashboard Cite

show abstract

“…At last, the preservation of the conventional bulk-boundary correspondence is demonstrated, but the gain/loss property of the chiral edge state under open boundary conditions (OBCs) depends on boundaries, which may be used in the control of its dynamics. This work deepens the understanding of gain/loss effects on topological insulators and may stimulate corresponding simulations with cold atoms as well as other experimental platforms, such as photonics [16,[41][42][43][44][45], nitrogen-vacancy centers [46,47], electrical circuits [48,49], and mechanical systems [50,51].…”

Section: Introductionmentioning

confidence: 83%

Gain/loss effects on spin-orbit coupled ultracold atoms in two-dimensional optical lattices

Xu,

Zhou,

Cheng

et al. 2022

Preprint

View full text Add to dashboard Cite

Due to the fundamental position of spin-orbit coupled ultracold atoms in the simulation of topological insulators, the gain/loss effects on these systems should be evaluated when considering the measurement or the coupling to the environment. Here, incorporating the mature gain/loss techniques into the experimentally realized spin-orbit coupled ultracold atoms in two-dimensional optical lattices, we investigate the corresponding non-Hermitian tight-binding model, evaluating the gain/loss effects on various properties of the system in the context of non-Hermitian physics. Under periodic boundary conditions, we analytically give, via block diagonalization, the topological phase diagram, which undergoes a non-Hermitian gapless interval instead of a point of the Hermitian counterpart, causing that the complex band inversion is just a necessary but not sufficient condition for the topological phase transition. A gauge-independent non-Hermitian Wilson-line method is developed for numerically calculating the non-Hermitian Chern number of a subspace consisting of multiple complex bands, because the nodal loops of the lower/upper two bands of the Hermitian counterpart can be split into exceptional loops in this non-Hermitian model. Under open boundary conditions, we find that the conventional bulk-boundary correspondence does not break down, but the dynamics of the chiral edge states depend on the boundary selection, which may be used for the control of edge dynamics.

show abstract

“…A noticeable exception is provided by the Hatano-Nelson model in the limiting case of unidirectional hopping [1], which is amenable for some analytical treatment. The realization of synthetic lattices with asymmetric hopping and controlled disorder, demonstrated in recent experiments [14,87,88], have stimulated a renewed interest in the understanding of the interplay among non-Hermiticity, topology and disorder [89][90][91][92] with potential impact to applications, such as in the design of non-Hermitian topological classical or quantum sensors [93].…”

Section: Introductionmentioning

confidence: 99%

Spectral deformations in non-Hermitian lattices with disorder and skin effect: A solvable model

Longhi

2021

Phys. Rev. B

View full text Add to dashboard Cite

We derive analytical results on energy spectral phase transitions and deformations in the simplest model of one-dimensional lattice displaying the non-Hermitian skin effect, namely the Hatano-Nelson model with unidirectional hopping, under on-site potential uncorrelated disorder in complex energy plane. While the energy spectrum under open boundary conditions (OBC) exactly reproduces the distribution of on-site potential disorder, the energy spectrum under periodic boundary conditions (PBC) undergoes spectral deformations, from one or more closed loops in the fully delocalized phase, with no overlap with the OBC spectrum, to a mixed spectrum (closed loops and some OBC energies) in the mobility edge phase, to a complete collapse toward the OBC spectrum in the bulk localized phase. Such transitions are observed as the strength of disorder is increased. Depending on the kind of disorder, different interesting behaviors are found. In particular, for continuous disorder with a radial distribution in complex energy plane it is shown that in the delocalized phase the energy spectrum under PBC is locked and fully insensitive to disorder, while transition to the bulk localized phase is signaled by the change of a topological winding number. When the disorder is described by a discrete distribution, the bulk localization transition never occurs, while topological phase transitions associated to PBC energy spectral splittings can be observed.

show abstract

Observation of arbitrary topological windings of a non-Hermitian band

Cited by 4 publications

References 52 publications

Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper model

Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper model

Gain/loss effects on spin-orbit coupled ultracold atoms in two-dimensional optical lattices

Spectral deformations in non-Hermitian lattices with disorder and skin effect: A solvable model

Contact Info

Product

Resources

About