Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

Zeng, Qi-Bo; Chen, Shu; Rong, Lü

doi:10.1103/physreva.95.062118

Cited by 109 publications

(55 citation statements)

References 51 publications

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“…Upon increasing L, the finite-size energy gap decreases from a purely real number to zero, at a certain L the imaginary part is developed and reaches a constant value 2γ x as indicated by Eq. (19). The result is quite similar to that in the non-Hermitian SSH model with only γ z [Sec.…”

Section: Non-hermitian Chern Insulator Modelsupporting

confidence: 76%

Finite-size effects in non-Hermitian topological systems

Chen

Zhou

et al. 2019

Phys. Rev. B

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We systematically investigate the finite-size effects in non-Hermitian one-dimensional (1D) Su-Schrieffer-Heeger (SSH) and two-dimensional (2D) Chern insulator models. In the Hermitian SSH system, the finite-size energy gap is always real and shows a monotonic-exponential decay as the chain length grows. In contrast, for the non-Hermitian SSH model, the non-Hermitian intra-cell hoppings can modify the localization lengths of bulk and end states, giving rise to a complex finitesize energy gap that exhibits an oscillating exponential decay as the chain length grows. However, the imaginary staggered on-site potentials in the SSH model only change the end-state energy, leaving the localization lengths of the system unchanged. In this case, the finite-size energy gap can undergo a transition from real values to imaginary values. We observed similar phenomena for the finite-size effect in 2D non-Hermitian Chern insulator systems. arXiv:1901.06820v2 [cond-mat.mes-hall]

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Section: Non-hermitian Chern Insulator Modelsupporting

confidence: 76%

Finite-size effects in non-Hermitian topological systems

Chen

Zhou

et al. 2019

Phys. Rev. B

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“…On the other hand, for real-energy on-site potential disorder a non-Hermitian delocalization transition is observed * stefano.longhi@polimi.it by application of an imaginary gauge field (Hatano-Nelson-Anderson model [23-26, 29, 33, 39, 46, 47, 49]). Other studies focused on several non-Hermitian extensions of diagonal or off-diagonal AAH models [31, 35-37, 40, 41, 43, 44, 47-50], with either commensurate or incommensurate potential, showing the impact of non-Hermiticity terms in the Hamiltonian on edge states and parity-time (PT ) symmetry breaking [35-37, 41, 43], on the Hofstadter butterfly spectrum [36], and on the localization properties of eigenstates [43,44,[47][48][49][50]. Recently, the topological nature of a metal-insulator phase transition found in an incommensurate PT -symmetric AAH model has been revealed [48].…”

Section: Introductionmentioning

confidence: 99%

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

Longhi

2019

Phys. Rev. B

150

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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.

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“…In the Hermitian case, the AAH Hamiltonian is topologically nontrivial because it can be mapped into a two-dimensional quantum Hall system on a square lattice [47][48][49][50]. A few recent studies have considered some non-Hermitian extensions of the AAH model [51][52][53][54][55][56], mainly with a commensurate potential and with open boundary conditions. Such numerical studies investigated how gain and loss distributions affect edge states and parity-time (PT ) symmetry breaking [51][52][53]55], the Hofstadter butterfly spectrum [52], and the localization properties of eigenstates [54,56].…”

mentioning

confidence: 99%

Topological Phase Transition in non-Hermitian Quasicrystals

2019

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The discovery of topological phases in non-Hermitian open classical and quantum systems challenges our current understanding of topological order. Non-Hermitian systems exhibit unique features with no counterparts in topological Hermitian models, such as failure of the conventional bulk-boundary correspondence and non-Hermitian skin effect. Advances in the understanding of the topological properties of non-Hermitian lattices with translational invariance have been reported in several recent studies, however little is known about non-Hermitian quasicrystals. Here we disclose topological phases in a quasicrystal with parity-time (PT ) symmetry, described by a non-Hermitian extension of the Aubry-André-Harper model. It is shown that the metal-insulating phase transition, observed at the PT symmetry breaking point, is of topological nature and can be expressed in terms of a winding number. A photonic realization of a non-Hermitian quasicrystal is also suggested.Introduction. The discovery of topological phases of matter has introduced a major twist in condensed matter physics [1, 2] with great impact in other areas of physics, such as photonics, atom optics, acoustics and mechanics [3][4][5][6][7][8]. Topological band theory classifies Hermitian topological systems depending on their dimensionality and symmetries [9, 10]. The bulk topological invariants are uniquely reflected in robust edge states localized at open boundaries. The ability to engineer non-Hermitian Hamiltonians, demonstrated in a series of recent experiments [11][12][13][14][15][16][17], and the related observation of unconventional topological boundary modes sparked a great interest to extend topological band theory to open systems . Striking features are the failure of the conventional bulk-boundary correspondence [27,31,35,[37][38][39], eigenstate condensation [30,31], non-Hermitian skin effect [33,37,38], and the sensitivity of the bulk spectra on boundary conditions [19,36,[39][40][41]. Most of previous studies have concerned with crystals, however little is know about topological properties of non-Hermitian quasicrystals. Quasicrystals (QCs) constitute an intermediate phase between fully periodic lattices and fully disordered media, showing a longrange order but no periodicity [42,43]. A paradigmatic model of a one-dimensional (1D) QC is provided by the Aubry-André-Harper (AAH) Hamiltonian [43][44][45], which is known to show a metal-insulator phase transition [44][45][46]. In the Hermitian case, the AAH Hamiltonian is topologically nontrivial because it can be mapped into a two-dimensional quantum Hall system on a square lattice [47][48][49][50]. A few recent studies have considered some non-Hermitian extensions of the AAH model [51][52][53][54][55][56], mainly with a commensurate potential and with open boundary conditions. Such numerical studies investigated how gain and loss distributions affect edge states and parity-time (PT ) symmetry breaking [51][52][53]55], the Hofstadter butterfly spectrum [52], and the localization properties of eig...

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Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

Cited by 109 publications

References 51 publications

Finite-size effects in non-Hermitian topological systems

Finite-size effects in non-Hermitian topological systems

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

Topological Phase Transition in non-Hermitian Quasicrystals

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