Classification of Exceptional Nodal Topologies Protected by $\mathcal{PT}$ Symmetry

Stålhammar, Marcus; Bergholtz, Emil J.

doi:10.48550/arxiv.2106.04582

Cited by 3 publications

(4 citation statements)

References 39 publications

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“…In the last decade, the topological nodal-knot semimetals in Hermitian systems [66][67][68][69][70][71][72][73][74][75] and non-Hermitian systems [42][43][44][45][53][54][55][56][57][58][59], have been studied in many previous work. The knotted structure of the non-Hermitian bands has also been proposed recently [23,31].…”

Section: B Infernal Knotsmentioning

confidence: 99%

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Degeneracy and defectiveness in non-Hermitian systems with open boundary

Fu,

Wan

2021

Preprint

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We develop a systematically general theory of one-dimensional (1D) non-Hermitian systems, elaborating the energy bands, the band degeneracy, and the defectiveness of eigenstates under open boundary condition. We analyze the band degeneracy and defectiveness of two typical 1D non-Hermitian models. We obtain the unusual presence and absence of the exceptional points in the generalized non-Hermitian Su-Schrieffer-Heeger model under open boundary condition. Beyond the general theory, we discover that there exist the infernal points in 1D non-Hermitian systems, where the energy spectra converge at some discrete energy values. We analyze two relevant 1D non-Hermitian models with the existence of infernal points. Moreover, we generalize the infernal points to the infernal knots in a four-dimensional systems. The general theory and the infernal points of non-Hermitian systems developed in this paper are also valid in Hermitian systems.

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Section: B Infernal Knotsmentioning

confidence: 99%

“…Recently, the knot theory has spread to the non-Hermitian systems, both on the energy band structure [23,31] and nodal points [42-45, 53, 59]. The exceptional Hopf-link [42][43][44][45]53] and higher-order EPs [51,[54][55][56][57][58][59] become new attractive courses in non-Hermitian systems.…”

Section: Introductionmentioning

confidence: 99%

Degeneracy and defectiveness in non-Hermitian systems with open boundary

Fu,

Wan

2021

Preprint

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“…without adjusting external parameters. However, various symmetries including PTsymmetry and chiral symmetry have been found to cut the number of parameters to be tweaked in half [45][46][47][48][49], thus suggesting the possibility of naturally observing symmetry-protected exceptional points up to fourth order.…”

mentioning

confidence: 99%

Fourth-Order Exceptional Points in Correlated Quantum Many-Body Systems

Crippa,

Budich,

Sangiovanni

2021

Preprint

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Non-Hermtian (NH) Hamiltonians effectively describing the physics of dissipative systems have become an important tool with applications ranging from classical meta-materials to quantum manybody systems. Exceptional points, the NH counterpart of spectral degeneracies, are among the paramount phenomena unique to the NH realm. While realizations of second-order exceptional points have been reported in a variety of microscopic models, higher-order ones have largely remained elusive in the many-body context, as they in general require fine tuning in high-dimensional parameter spaces. Here, we propose a microscopic model of correlated fermions in three spatial dimensions and demonstrate the occurrence of interaction-induced fourth-order exceptional points that are protected by chiral symmetry. We demonstrate their stability against symmetry breaking perturbations and investigate their characteristic analytical and topological properties.

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“…These excetpional phases are charaterized by a local topological invariant dependent on the EPs [19,[34][35][36]. Based on non-spatial symmetries, the local structure of EPs has been studied [36][37][38].…”

mentioning

confidence: 99%

Non-Hermitian spatial symmetries and their stabilized normal and exceptional topological semimetals

Rui,

Zheng,

Wang

et al. 2021

Preprint

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Without the constraint imposed by Hermiticity, non-Hermitian systems enjoy greater freedom than Hermitian ones. While the non-Hermitian ramification of non-spatial (internal) symmetries has been revealed, spatial symmetries remain to be explored. Here, we identify intrinsically non-Hermitian spatial symmetries using the same reasoning as non-spatial symmetry ramification. The symmetry endows exceptional topological semimetals with global topological structures, by preserving exceptional points but altering their topological invariants nonlocally. Furthermore, the global band configuration in the bulk is strongly constrained by non-Hermitian spatial symmetry, due to the intertwining of left and right eigen-systems at symmetry-related locations in momentum space. We illustrate our theory using two novel topological phases in three dimensions (3D): exceptional unconventional Weyl semimetals and exceptional triple-point semimetals, in which the global structures of exceptional points, exceptional lines, and higher-order exceptional points are stabilized by one or more non-Hermitian spatial symmetries. We propose a cold-atom experiment to realize the exceptional unconventional Weyl semimetals.

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Classification of Exceptional Nodal Topologies Protected by $\mathcal{PT}$ Symmetry

Cited by 3 publications

References 39 publications

Degeneracy and defectiveness in non-Hermitian systems with open boundary

Degeneracy and defectiveness in non-Hermitian systems with open boundary

Fourth-Order Exceptional Points in Correlated Quantum Many-Body Systems

Non-Hermitian spatial symmetries and their stabilized normal and exceptional topological semimetals

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