Darboux operators for linear first-order multi-component equations in arbitrary dimensions

Schulze-Halberg, Axel

doi:10.2478/s11534-013-0242-0

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2024

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“…This was discussed for stationary one-dimensional 2 × 2 Dirac equations in [17] and for nonstationary equations in [18]. Diverse extensions of Darboux transformation for Dirac operators were proposed for systems in polar coordinates [19], higher dimensions [20,21], and higher spin models [22]. A further generalization of the intertwining relations for Dirac operators was discussed in [23].…”

Section: Introductionmentioning

confidence: 99%

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Reflectionless pseudospin-1 Dirac systems via Darboux transformation and flat band solutions

Jakubský,

Zelaya

2024

Phys. Scr.

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This manuscript explores the Darboux transformation employed in the construction of exactly solvable models for pseudospin-one particles described by the Dirac-type equation. We focus on the settings where a flat band of zero energy is present in the spectrum of the initial system. Using the flat band state as one of the seed solutions substantially improves the applicability of the Darboux transformation, for it becomes necessary to ensure the Hermiticy of the new Hamiltonians. This is illustrated explicitly in four examples, where we show that the new Hamiltonians can describe quasi-particles in Lieb lattice with inhomogeneous hopping amplitudes.

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Section: Introductionmentioning

confidence: 99%

“…if the seed matrix (24) is used. Now, let us show that one can still use the factorization energies in (22) and achieve the desired Hermiticity, provided that a flat-band solution is employed. To this end, let us make an alternative choice of seed solutions by fixing the seed matrix as…”

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confidence: 99%