Topology of multipartite non-Hermitian one-dimensional systems

Nehra, Ritu; Roy, Dibyendu

doi:10.1103/physrevb.105.195407

Cited by 19 publications

(8 citation statements)

References 92 publications

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“…. Furthermore even in the periodic gauge, Zak's expression (30) does not yields the correct value for the geometric phase, since ( 30) is devoid of the non-trivial contribution due to ( ) ( )…”

Section: Single-particle Casementioning

confidence: 99%

“…A careful observation shows that the expression (25) of the Pancharatnam-Zak phase coincides with the Zak phase (30), not in the periodic gauge 0 χ = , but in the gauge wherein χ is defined such that ( ) ( )…”

Section: Single-particle Casementioning

confidence: 99%

“…The geometrical phase for the filled band case is properly formulated, and its physical implications are discussed. In our other studies, a generalisation of the Pancharathnam-Zak phase has provided valuable insights and has captured the topological phases of the undriven and periodically driven non-Hermitian bipartite and multipartite Su-Schrieffer-Heeger (SSH) model[29] [30]. In summary, we argue in this paper a requirement of generalized cyclicity for adequately describing the geometric phase for particle(s) in the 1D periodic lattice and construct the gauge-invariant Pancharatnam-Zak phase whose absolute value for each band in topologically trivial and non-trivial phases is independent of the choice of the origin of the unit cell.…”

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confidence: 99%

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A Gauge-Invariant Geometric Phase for Electrons in a One-Dimensional Periodic Lattice

Vyas¹,

Roy²

2023

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Here the notion of geometric phase acquired by an electron in a one-dimensional periodic lattice as it traverses the Bloch band is carefully studied. Such a geometric phase is useful in characterizing the topological properties and the electric polarization of the periodic system. An expression for this geometric phase was first provided by Zak, in a celebrated work three decades ago. Unfortunately, Zak's expression suffers from two shortcomings: its value depends upon the choice of origin of the unit cell, and is gauge dependent. Upon careful investigation of the time evolution of the system, here we find that the system displays cyclicity in a generalized sense wherein the physical observables return in the course of evolution, rather than the density matrix. Recognition of this generalized cyclicity paves the way for a correct and consistent expression for the geometric phase in this system, christened as Pancharatnam-Zak phase. Pancharatnam-Zak geometric phase does not suffer from the shortcomings of Zak's expression, and correctly classifies the Bloch bands of the lattice. A naturally filled band extension of the Pancharatnam-Zak phase is also constructed and studied.

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Section: Single-particle Casementioning

confidence: 99%

Section: Single-particle Casementioning

confidence: 99%

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confidence: 99%

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A Gauge-Invariant Geometric Phase for Electrons in a One-Dimensional Periodic Lattice

Vyas¹,

Roy²

2023

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“…In the following, we apply the exceptional classification framework to 1D systems. As an example, we consider the nonreciprocal Su-Schrieffer-Heeger (SSH) model [39][40][41][42][43] , where the Hamiltonian is given as…”

Section: Non-reciprocal Ssh Modelmentioning

confidence: 99%

Exceptional Classifications of Non-Hermitian Systems

Park

Ryu

Han

et al. 2023

Preprint

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Eigenstate coalescence in non-Hermitian systems is widely observed in diverse scientific domains encompassing optics and open quantum systems. Recent investigations have revealed that adiabatic encircling of exceptional points (EPs) leads to a nontrivial Berry phase in addition to an exchange of eigenstates. Based on these phenomena, we propose in this work an exhaustive classification framework for EPs in non-Hermitian physical systems. In contrast to previous classifications that only incorporate the eigenstate exchange effect, our proposed classification gives rise to finer Z2 classifications depending on the presence of a π Berry phase after the encircling of the EPs. Moreover, by mapping arbitrary one-dimensional systems to the adiabatic encircling of EPs, we can classify one-dimensional non-Hermitian systems characterized by topological phase transitions involving EPs. Applying our exceptional classification to various one-dimensional models, such as the non-reciprocal Su–Schrieffer–Heeger (SSH) model, we exhibit the potential for enhancing the understanding of topological phases in non-Hermitian systems. Additionally, we address exceptional bulk-boundary correspondence and the emergence of distinct topological boundary modes in non-Hermitian systems.

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“…[9] The SSH model, which is not as simple as it looks, has unusual physical connotations. In the past few decades, extensive studies have investigated the SSH model and its variants, such as an SSH model with nextnearest-neighbor hopping, [10][11][12] the SSH3 and SSH4 models with short-and long-range hopping, [13][14][15][16][17][18][19][20][21] an SSH model with spin-orbit coupling, [22,23] and two coupled SSH chains. [24][25][26] The basic SSH model has two alternating hopping amplitudes that do not include the potential energy at the atomic sites.…”

Section: Introductionmentioning

confidence: 99%

Topological properties of tetratomic Su–Schrieffer–Heeger chains with hierarchical long-range hopping

Wang

Tang

et al. 2023

Chinese Phys. B

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A new generalized Su-Schrieffer-Heeger model with hierarchical long-range hoppings based on the one-dimensional tetratomic chain is proposed. The properties of the topological states and phase transition, depending on the cointeraction of the intracell and intercell hoppings, are investigated by the phase diagram of the winding number. It is found that topological states with large positive/negative winding numbers can be readily generated in the system. The properties of the topological states can be verified by the ring-type structures in the trajectory diagram of the complex plane. The topological phase transition is strongly related with the opening up or closure of the energy bandgap at the center/boundaries of the Brillouin zone. Finally, the feature of the non-zeroenergy edge states at the ends of the finite system is revealed and matched with the bulk-boundary correspondence.

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Topology of multipartite non-Hermitian one-dimensional systems

Cited by 19 publications

References 92 publications

A Gauge-Invariant Geometric Phase for Electrons in a One-Dimensional Periodic Lattice

A Gauge-Invariant Geometric Phase for Electrons in a One-Dimensional Periodic Lattice

Exceptional Classifications of Non-Hermitian Systems

Topological properties of tetratomic Su–Schrieffer–Heeger chains with hierarchical long-range hopping

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