Non-Hermitian Kitaev chain with complex on-site potentials

Zeng, Qi-Bo; Zhu, Biyun; Chen, Shu; You, Li; Rong, Lü

doi:10.1103/physreva.94.022119

Cited by 57 publications

(33 citation statements)

References 44 publications

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“…With appropriate conditions, these PT -symmetric Hamiltonians can have purely real energy spectra [7,8]. The properties of PT -symmetric Hamiltonians and the corresponding breaking of this symmetry in many different non-Hermitian systems have been extensively studied [9][10][11][12][13][14][15][16][17][18][19]. Experimentally, there are also many different kinds of realizations of open systems in optical [20][21][22][23], mechanical [24], and electrical [25] setups, which endow the non-Hermitian Hamiltonians more practical signifi-cance.…”

Section: Introductionmentioning

confidence: 99%

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

2017

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We investigate the Anderson localization in non-Hermitian Aubry-André-Harper (AAH) models with imaginary potentials added to lattice sites to represent the physical gain and loss during the interacting processes between the system and environment. By checking the mean inverse participation ratio (MIPR) of the system, we find that different configurations of physical gain and loss have very different impacts on the localization phase transition in the system. In the case with balanced physical gain and loss added in an alternate way to the lattice sites, the critical region (in the case with p-wave superconducting pairing) and the critical value (both in the situations with and without p-wave pairing) for the Anderson localization phase transition will be significantly reduced, which implies an enhancement of the localization process. However, if the system is divided into two parts with one of them coupled to physical gain and the other coupled to the corresponding physical loss, the transition process will be impacted only in a very mild way. Besides, we also discuss the situations with imbalanced physical gain and loss and find that the existence of random imaginary potentials in the system will also affect the localization process while constant imaginary potentials will not.

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Section: Introductionmentioning

confidence: 99%

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

2017

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“…[95] and Refs. [36] and [68], respectively, to our attention. This work was supported by a Grant-in-Aid for Scientific Research on Innovative Areas "Topological Materials Science" (KAKENHI Grant No.…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…[32] assumes no symmetry other than parity-time symmetry and mentions possible exceptions of its theorem due to particle-hole or point-group symmetry. In fact, a p-wave topological superconducting wire with balanced gain and loss, which is described by a non-Hermitian extension of the Kitaev chain [85] with parity-time symmetry, can possess the entirely real spectrum even in the presence of Majorana edge states [36,39,42]. By contrast, non-Hermitian topological insulators with entirely real spectra have yet to be known.…”

Section: Introductionmentioning

confidence: 99%

Real spectra in non-Hermitian topological insulators

Kawabata

Sato

2020

Phys. Rev. Research

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Spectra of bulk or edges in topological insulators are often made complex by non-Hermiticity. Here, we show that symmetry protection enables entirely real spectra for both bulk and edges even in non-Hermitian topological insulators. In particular, we demonstrate the entirely real spectra without non-Hermitian skin effects due to a combination of pseudo-Hermiticity and Kramers degeneracy. This protection relies on nonspatial fundamental symmetry and has stability against disorder. As an illustrative example, we investigate a non-Hermitian extension of the Bernevig-Hughes-Zhang model. The helical edge states exhibit oscillatory dynamics due to their nonorthogonality as a unique non-Hermitian feature.

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“…The Hamiltonian, Eq. ( 1), can be mapped to the free spinless fermion model with complex chemical potential [100] by Jordan-Wigner transformation [101][102][103][104] (see Appendix A)…”

Section: A Exact Solutionmentioning

confidence: 99%

“…( 7) belongs to BDI in the periodic table of non-Hermitian topological phases [53]. Moreover, H F (k) encompasses the inversion symmetry U I H(k)U −1 I = H(−k) with U I = σ z , which manifests the correspondence between the bulk topological invariant and the number of Majorana edge modes under the open boundary condition [53,100].…”

Section: A Exact Solutionmentioning

confidence: 99%

Dissipative Floquet Dynamical Quantum Phase Transition

Naji,

Jafari,

Jafari

et al. 2021

Preprint

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Non-Hermitian Hamiltonians provide a simple picture for inspecting dissipative systems with natural or induced gain and loss. We investigate the Floquet dynamical phase transition in the dissipative periodically time driven XY and extended XY models, where the imaginary terms represent the physical gain and loss during the interacting processes with the environment. The time-independent effective Floquet non-Hermitian Hamiltonians disclose three regions by analyzing the non-Hermitian gap: pure real gap (real eigenvalues), pure imaginary gap, and complex gap. We show that each region of the system can be distinguished by the complex geometrical non-adiabatic phase. We have discovered that in the presence of dissipation, the Floquet dynamical phase transitions (FDPTs) still exist in the region where the time-independent effective Floquet non-Hermitian Hamiltonians reveal real eigenvalues. Opposed to expectations based on earlier works on quenched systems, our findings show that the existence of the non-Hermitian topological phase is not an essential condition for dissipative FDPTs (DFDPTs). We also demonstrate the range of driven frequency, over which the DFDPTs occur, narrows down by increasing the dissipation coupling and shrinks to a single point at the critical value of dissipation. Moreover, quantization and jumps of the dynamical geometric phase reveals the topological characteristic feature of DFDPTs in the real gap region where confined to exceptional points.

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Non-Hermitian Kitaev chain with complex on-site potentials

Cited by 57 publications

References 44 publications

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

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

Real spectra in non-Hermitian topological insulators

Dissipative Floquet Dynamical Quantum Phase Transition

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