Exceptional Bound States and negative Entanglement Entropy

Lee, Ching Hua

doi:10.48550/arxiv.2011.09505

Cited by 3 publications

(3 citation statements)

References 50 publications

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“…The spectra of non-Hermitian systems lie in the 2D complex plane, and can exhibit intriguing geometric and topological spectral transitions. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] In particular, it is known [17][18][19][20] that if the spectrum under periodic boundary conditions (PBCs) is a loop that encloses a nonvanishing region, the spectrum of the same system under semi-infinite boundary conditions (SIBCs) will fill up the interior of this loop. This intriguing fact is due to the non-local nature of the non-Hermitian skin effect (NHSE), which has inspired numerous theoretical and experimental [21][22][23][24][25]25,[25][26][27][28][29][30][31][32][33][34][35] developments and challenged various longheld paradigms in physics.…”

Section: Introductionmentioning

confidence: 99%

Filling up complex spectral regions through non-Hermitian disordered chains

Hui

Lee

2022

Chinese Phys. B

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Eigenspectra that fill regions in the complex plane have been intriguing to many, inspiring research from random matrix theory to esoteric semi-infinite bounded non-Hermitian lattices. In this work, we propose a simple and robust ansatz for constructing models whose eigenspectra fill up generic prescribed regions. Our approach utilizes specially designed non-Hermitian random couplings that allow the co-existence of eigenstates with a continuum of localization lengths, mathematically emulating the effects of semi-infinite boundaries. While some of these couplings are necessarily long-ranged, they are still far more local than what is possible with known random matrix ensembles. Our ansatz can be feasibly implemented in physical platforms such as classical and quantum circuits, and harbors very high tolerance to imperfections due to its stochastic nature.

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Section: Introductionmentioning

confidence: 99%

Filling up complex spectral regions through non-Hermitian disordered chains

Hui

Lee

2022

Chinese Phys. B

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“…Nonhermicity has brought about a plethora of interesting new phenomena [1][2][3][4][5][6][7][8][9][10][11][12][13][14], of which the non-Hermitian skin-effect (NHSE) [15][16][17][18][19][20][21][22][23][24][25][26] (i.e, extreme localization of the eigenstates to a boundary) has galvanized various reformulations of the conventional concepts of the Brillouin zone (BZ) and bulk-boundary correspondence (BBC) [27,28]. While the BBC can already be broken with a single asymmetric non-Hermitian coupling, the more interesting interplay between multiple asymmetric non-Hermitian couplings has not been thoroughly explored.…”

Section: Introductionmentioning

confidence: 99%

Unconventional node voltage accumulation in generalized topolectrical circuits with multiple asymmetric couplings

Rafi-Ul-Islam,

Siu,

Sahin

et al. 2021

Preprint

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A non-Hermitian system is characterized by the violation of energy conservation. As a result of unbalanced gain or loss in the forward and backward directions due to non-reciprocal couplings, the eigenmodes of such systems exhibit extreme localization, also known as non-Hermitian skin effect (NHSE). This work explores unconventional scenarios where the interplay of multiple asymmetric couplings can cause the NHSE to vanish, with the admittance spectra taking identical dispersion under open boundary conditions (OBC) and periodic boundary conditions (PBC). This is unlike known non-Hermitian models where the NHSE vanishes only when the non-Hermiticity is turned off. We derive general conditions for the NHSE, with the overall eigenmode localization determined by the geometric mean of the cumulative contributions of all asymmetric coupling segments. In the limit of large unit cells, our results provide a route towards the NHSE caused by asymmetric hopping textures, rather than single asymmetric hoppings alone. Furthermore, our generalized model can be transformed into a square-root lattice simply by tuning the coupling capacitors, where the topological edge states occur at a non-zero admittance, in contrast to the zero-admittance states of conventional topological insulators. We provide explicit electrical circuit setups for realizing our observations, which also extend to other established platforms such as photonics, mechanics, optics and quantum circuits.

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“…However, most topological systems in reality experience a finite energy exchange from surroundings and an inevitable loss or gain of energy [21]. The non-conservation of energy results in non-Hermitian systems [22][23][24][25][26][27][28][29][30][31], where the usual topological definitions and classifications of matter may no longer be applicable [32,33]. Interestingly, non-Hermitian systems host a plethora of unusual phenomena that include exceptional points [23,34,35], nodal rings [36,37], extensive localization of eigenstates [38][39][40][41], unidirectional transport [42,43], and the amplification and attenuation of quantum signals [44,45].…”

Section: Introductionmentioning

confidence: 99%

Critical hybridization of skin modes in coupled non-Hermitian chains

Rafi-Ul-Islam¹,

Siu²,

Sahin³

et al. 2021

Preprint

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Non-Hermitian topological systems exhibit a plethora of unusual topological phenomena that are absent in the Hermitian systems. One of these key features is the extreme eigenstate localization of eigenstates, also known as non-Hermitian skin effect (NHSE), which occurs in open chains. However, many new and peculiar non-Hermitian characteristics of the eigenstates and eigenvlaues that emerge when two such non-Hermitian chains are coupled together remain largely unexplored. Here, we report various new avenues of eigenstate localization in coupled non-Hermitian chains with dissimilar inverse skin lengths in which the NHSE can be switched on and off by the inter-chain coupling amplitude. A very small inter-chain strength causes the NHSE to be present at both ends of an anti-symmetric coupled system because of the weak hybridization of the eigenstates of the individual chains. The eigenspectrum under open boundary conditions (OBC) exhibits a discontinuous jump known as the critical NHSE (CNHSE) as its size increases. However, when the hybridization between eigenstates becomes significant in a system with strong inter-chain coupling, the NHSE and CNHSE vanish. Moreover, a peculiar " half-half skin localization" occurs in composite chains with opposite signs of inverse decay lengths, where half of the eigenstates are exponentially localized at one chain and the remainder of the eigenstates on the other chain. Our results provide a new twist and insights for non-Hermitian phenomena in coupled non-Hermitian systems.

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Exceptional Bound States and negative Entanglement Entropy

Cited by 3 publications

References 50 publications

Filling up complex spectral regions through non-Hermitian disordered chains

Filling up complex spectral regions through non-Hermitian disordered chains

Unconventional node voltage accumulation in generalized topolectrical circuits with multiple asymmetric couplings

Critical hybridization of skin modes in coupled non-Hermitian chains

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