Delocalization of a non-Hermitian quantum walk on random media in one dimension

Hatano, Naomichi; Obuse, Hideaki

doi:10.1016/j.aop.2021.168615

Cited by 11 publications

(4 citation statements)

References 22 publications

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“…Consequently, it would be possible to apply the biorthogonal fidelity susceptibility to understand the nature of phase transitions in non-integrable non-Hermitian many-body models. Moreover, it would be more interesting to know whether the biorthogonal fidelity susceptibility is useful to detect the universal class for the real-complex spectral transition of non-Hermitian many-body models [39] or the localization-delocalization transition of non-Hermitian quantum systems [108][109][110] in the future.…”

Section: And the Paramagnetic Phase Atmentioning

confidence: 99%

Biorthogonal quantum criticality in non-Hermitian many-body systems

2021

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We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of the ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a secondorder phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.

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Section: And the Paramagnetic Phase Atmentioning

confidence: 99%

Biorthogonal quantum criticality in non-Hermitian many-body systems

2021

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“…The notion of non-Hermiticity and its interplay with disorder has been a recent subject of wide-ranging interest. The effect of disorder on the inherently non-Hermitian Hatano Nelson model [66][67][68][69][70][71] has been studied recently, where disorder has been introduced in the hopping to obtain interesting physics, such as disorder-driven phase transitions from an extended phase to a bulk localized phase [72] and an non-Hermitian Anderson skin effect (NHASE), where disorder gives rise to a skin effect [73], and more. Some studies of the non-Hermitian Su-Schrieffer-Heeger (SSH) model [74][75][76][77][78][79][80] have also been performed, where disorder has been introduced in the hopping to find a non-Hermitian topological (NH top) Anderson insulating phase [81].…”

Section: Introductionmentioning

confidence: 99%

Interplay of disorder and point-gap topology: Chiral modes, localization, and non-Hermitian Anderson skin effect in one dimension

2022

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Symmetry-protected spectral topology in extended non-Hermitian quantum systems has interesting manifestations such as dynamically anomalous chiral currents and skin effect. In this paper, we study the interplay between symmetries and disorder in a paradigmatic model for spectral topology-the nonreciprocal Su-Schrieffer-Heeger model. We consider the effect of on-site perturbations (both real and purely imaginary) that explicitly break the sublattice symmetry. Such symmetry-breaking terms can retain a nontrivial spectral topology but lead to a different symmetry class. We numerically study the effect of disorder in on-site and nonreciprocal hopping terms. Using a real-space winding number that is self-averaging and quantized, we investigate the impact of disorder on the spectral topology and associated anomalous chiral modes under periodic boundary conditions. We discover a remarkable robustness of chiral current and its self-averaging nature under disorder. The value of the chiral current retains the clean system value, is independent of disorder strength, and is tracked completely by the real-space winding number for class A which has no symmetries, and class AIII, which has a sublattice symmetry. In class D † , which has PT -symmetric on-site gain and loss terms, we find that the disorder-averaged current is not robust while the winding number is robust. We study the localization physics using the inverse participation ratio and local density of states. As the disorder strength is increased, a mobility-edge phase with a finite winding appears. The abrupt vanishing of the winding number marks a transition from a partially localized to a fully localized phase. Under open boundary conditions, we similarly observe a series of transitions through skin effect-partial skin effect-no skin effect phases. Further, we study the non-Hermitian Anderson skin effect (NHASE) for different symmetry classes, where the system without skin effect develops a disorder-driven skin effect at intermediate disorder values. Remarkably, while NHASE is present for different classes, the real-space winding number shows a direct correspondence with it only when all symmetries are broken.

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“…The notion of non-Hermiticity and its interplay with disorder has been a recent subject of wide ranging interest. The effect of disorder on the inherently non-Hermitian Hatano Nelson model [61][62][63][64][65][66] has been studied recently, where disorder has been introduced in the hopping to obtain interesting physics, such as disorder driven phase transitions from an extended phase to a bulk localized phase 67 and an non-Hermitian Anderson skin effect, where disorder gives rise to a skin effect 68 , and more. Some studies of the non-Hermitian Su-Schrieffer-Heeger (SSH) model [69][70][71][72][73][74][75] have also been performed, where disorder has been introduced in the hopping to find a non-Hermitian topological Anderson insulating phase 76 .…”

Section: Introductionmentioning

confidence: 99%

Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension

Sarkar,

Hegde,

Narayan

2022

Preprint

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Symmetry-protected spectral topology in extended non-Hermitian quantum systems has interesting manifestations such as dynamically anomalous chiral currents and skin effect. In this work, we study the interplay between symmetries and disorder in a paradigmatic model for spectral topology -the non-reciprocal Su-Schrieffer-Heeger model. We consider the effect of on-site perturbations (both real and purely imaginary) that explicitly break the sub-lattice symmetry. Such symmetry-breaking terms can retain a non-trivial spectral topology but lead to a different symmetry class. We numerically study the effect of disorder in on-site and non-reciprocal hopping terms. Using a real-space winding number that is self-averaging and quantized, we investigate the impact of disorder on the spectral topology and associated anomalous chiral modes under periodic boundary conditions. We discover a remarkable robustness of chiral current and its self-averaging nature under disorder. The value of the chiral current retains the clean system value, is independent of disorder strength and is tracked completely by the real-space winding number for class A which has no symmetries, and class AIII, which has a sub-lattice symmetry. In class D † , which has P T -symmetric on-site gain and loss terms, we find that the disorder-averaged current is not robust while the winding number is robust. We study the localization physics using the inverse participation ratio and local density of states. As the disorder strength is increased, a mobilityedge phase with a finite winding appears. The abrupt vanishing of the winding number marks a transition from a partially localized to a fully localized phase. Under open boundary conditions, we similarly observe a series of transitions through skin effect-partial skin effect-no skin effect phases. Further, we study the non-Hermitian Anderson skin effect (NHASE) for different symmetry classes, where the system without skin effect develops a disorder-driven skin effect at intermediate disorder values. Remarkably while NHASE is present for different classes, the real-space winding number shows a direct correspondence with it only when all symmetries are broken.

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Delocalization of a non-Hermitian quantum walk on random media in one dimension

Cited by 11 publications

References 22 publications

Biorthogonal quantum criticality in non-Hermitian many-body systems

Biorthogonal quantum criticality in non-Hermitian many-body systems

Interplay of disorder and point-gap topology: Chiral modes, localization, and non-Hermitian Anderson skin effect in one dimension

Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension

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