Machine learning topological invariants of non-Hermitian systems

Zhang, Ling-Feng; Tang, Ling-Zhi; Huang, Zhi-Hao; Zhang, Guo-Qing; Huang, Wei; Zhang, Dan-Wei

doi:10.48550/arxiv.2009.04058

Cited by 3 publications

(5 citation statements)

References 69 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note added-After finalizing this work, we became aware of a complementary study by Zhang et al [62]. Where overlapping, our results are consistent with theirs.…”

supporting

confidence: 81%

Machine learning non-Hermitian topological phases

Narayan

2021

Phys. Rev. B

View full text Add to dashboard Cite

Non-Hermitian topological phases have gained widespread interest due to their unconventional properties, which have no Hermitian counterparts. In this work, we propose to use machine learning to identify and predict non-Hermitian topological phases, based on their winding number. We consider two examples -non-Hermitian Su-Schrieffer Heeger model in one dimension and non-Hermitian nodal line semimetal in three dimensions -to demonstrate the use of neural networks to accurately characterize the topological phases. We show that for the one dimensional model, a fully connected neural network gives an accuracy greater than 99.9%, and is robust to the introduction of disorder. For the three dimensional model, we find that a convolutional neural network accurately predicts the different topological phases.

show abstract

“…Note added-After finalizing this work, we became aware of a complementary study by Zhang et al [62]. Where overlapping, our results are consistent with theirs.…”

supporting

confidence: 81%

Machine learning non-Hermitian topological phases

Narayan

2021

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…Recently, machine learning fuelled by algorithmic advances and increasing computer power [480] has been proven useful for designing and predicting various topological phases of matter [481][482][483][484]. It is shown that physical properties of the Hatano-Nelson models, the Aubry-André-Harper models [485], the 1D non-Hermitian SSH models and the 3D non-Hermitian semimetals [486] (nodal lines) can be predicted by identifying the non-Hermitian topological indicators in terms of fully connected neural networks (with the accuracy 99.9%) or convolutional neural networks (with the accuracy 99.8%). Unsupervised learning has also been proposed to classify non-Hermitian skin effects by distinguishing the vanishing diffusion probabilities, which guides both theories and experiments [487].…”

Section: Othersmentioning

confidence: 99%

Topological physics of non-Hermitian optics and photonics: a review

Wang

Zhang

Hua

et al. 2021

J. Opt.

View full text Add to dashboard Cite

The notion of non-Hermitian optics and photonics rooted in quantum mechanics and photonic systems has recently attracted considerable attention ushering in tremendous progress on theoretical foundations and photonic applications, benefiting from the flexibility of photonic platforms. In this review, we first introduce the non-Hermitian topological physics from the symmetry of matrices and complex energy spectra to the characteristics of Jordan normal forms, exceptional points, biorthogonal eigenvectors, Bloch/non-Bloch band theories, topological invariants and topological classifications. We further review diverse non-Hermitian system branches ranging from classical optics, quantum photonics to disordered systems, nonlinear dynamics and optomechanics according to various physical equivalences and experimental implementations. In particular, we include cold atoms in optical lattices in quantum photonics due to their operability at quantum regimes. Finally, we summarize recent progress and limitations in this emerging field, giving an outlook on possible future research directions in theoretical frameworks and engineering aspects.

show abstract

“…The Ref. [22,[25][26][27][28][29] focus on the Su-Schrieffer-Heeger (SSH) model [31,32] which is also the subject of this work.…”

Section: Introductionmentioning

confidence: 99%

“…Ref. [21,22,[25][26][27][28][29][30] are examples of recent work on identifying topological phases and phase transitions using either neural networks or diffusion maps. The Ref.…”

mentioning

confidence: 99%

“…The Ref. [22,[25][26][27][28][29] focus on the Su-Schrieffer-Heeger (SSH) model [31,32] which is also the subject of this work.The SSH model was introduced as a model for polyacetylene and is a simple extensively studied example of a model for a topological insulator [33,34]. The basic model consists of electrons (taken to be spinless) hopping on a one-dimensional lattice.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Exploring phases of the Su-Schrieffer-Heeger model with tSNE

Woloshyn

2021

Preprint

View full text Add to dashboard Cite

T-distributed stochastic neighborhood embedding (tSNE) is used as a tool to reveal the phase diagram of the Su-Schrieffer-Heeger model and some of its extended and non-Hermitian variants. Bloch vectors calculated at different points in the parameter space are mapped to a two-dimensional reduced space. The clusters in the reduced space are used to visualize different phase regions included in the input. The tSNE mapping is shown to be effective even in the challenging case of the non-Hermitian extended model where five different phases are present. An example of using wavefunction input, instead of Bloch vectors, is presented also. I. INTRODUCTIONMachine learning is being increasingly utilized in physics [1,2]. Examples of applications include event classification [3-5] and anomaly detection [6,7] in the analysis of particle physics experiments, aiding observations in astronomy [8], and the study of phases in condensed matter systems [9][10][11][12]. The focus here on the last topic, phases of matter.Many different machine learning methods have been applied to the exploration of phases and phase transitions. These include neural networks [13][14][15][16], principal component analysis [17,18], support vector machines [19] and diffusion maps [20][21][22]. In an interesting recent work, Yang et al. [23] suggested the use of t-distributed stochastic neighborhood embedding (tSNE) as an unsupervised learning method to obtain a visualization of phase diagrams and used this method to study a number of one-dimensional quantum spin systems.The idea of using unsupervised learning methods to reveal phases is particularly appealing. Specifically, topological phases [24] which can not be characterized by local order parameters can be studied without a priori input of domain knowledge. Ref. [21,22,[25][26][27][28][29][30] are examples of recent work on identifying topological phases and phase transitions using either neural networks or diffusion maps. The Ref. [22,[25][26][27][28][29] focus on the Su-Schrieffer-Heeger (SSH) model [31,32] which is also the subject of this work.The SSH model was introduced as a model for polyacetylene and is a simple extensively studied example of a model for a topological insulator [33,34]. The basic model consists of electrons (taken to be spinless) hopping on a one-dimensional lattice. The nearest-neighbor hopping amplitudes are taken to be staggered (see, for example, Fig. 1.1 in [33]) so the lattice can be divided into two-site units cells. Some details of the model are given in Sec. III.The SSH model can be extended by introducing longer range interactions. The extended SSH model considered here allows for the addition of next-next-nearest neighbor hopping terms [28,35]. A different type of modification of the model which has received considerable recent attention is to allow nonreciprocal intra-cell hoping [36,37]. This leads to a non-Hermitian Hamiltonian and the appearance of topological phases with fractional winding number [37].In this paper the tSNE algorithm, which has been used to s...

show abstract

Machine learning topological invariants of non-Hermitian systems

Cited by 3 publications

References 69 publications

Machine learning non-Hermitian topological phases

Machine learning non-Hermitian topological phases

Topological physics of non-Hermitian optics and photonics: a review

Exploring phases of the Su-Schrieffer-Heeger model with tSNE

Contact Info

Product

Resources

About