Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials

Burrello, Michele; Fulga, Ion Cosma; Lepori, Luca; Trombettoni, Andrea

doi:10.1088/1751-8121/aa8d26

Cited by 8 publications

(7 citation statements)

References 73 publications

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“…Indeed, these 2D models (connected by an interpolating pattern [41]) are also related with genuine Weyl semimetals by a projection along one axis. Reversely, by stacking the former models and adding suitable tunnelings along the stacking direction, one can obtain the latter ones [42][43][44][45] (in this way, anisotropic and non-linear dispersions can be also obtained [46][47][48]).…”

Section: Weyl Spinors On Lattice Systemsmentioning

confidence: 99%

Synthesis of Majorana mass terms in low-energy quantum systems

et al. 2018

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We discuss the problem of how Majorana mass terms can be generated in low-energy systems. We show that, while these terms imply the Majorana condition, the opposite is not always true when more than one flavour is involved. This is an important aspect for the low-energy realizations of the Majorana mass terms exploiting superfluid pairings, because in this case the Majorana condition is not implemented in the spinor space, but in an internal (flavour) space. Moreover, these mass terms generally involve opposite effective chiralities, similarly to a Dirac mass term. The net effect of these features is that the Majorana condition does not imply a Majorana mass term. Accordingly the obtained Majorana spinors, as well as the resulting symmetry breaking pattern and low-energy spectrum, are qualitatively different from the ones known in particle physics. This result has important phenomenological consequences, e.g. implies that these mass terms are unsuitable to induce an effective see-saw mechanism, proposed to give mass to neutrinos. Finally, we introduce and discuss schemes based on space-dependent pairings with nonzero total momentum to illustrate how genuine Majorana mass terms may emerge in low-energy quantum systems.

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Section: Weyl Spinors On Lattice Systemsmentioning

confidence: 99%

Synthesis of Majorana mass terms in low-energy quantum systems

et al. 2018

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“…Varying the magnetic flux: To study the model (2) it is convenient to choose the Hasegawa gauge [19] A(r) = Φ(0, x−y, y−x) for the definition of the θ phases (see [52] and Appendix A for further details). In the following the behaviour of the DOS and the properties and location of the VH singularities is studied for different values of n, starting from n = 2 and increasing n.…”

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confidence: 99%

“…We observe that with k ∈ MBZ the allowed values for the momenta are N/n 2 , and for each of them the matrix to be diagonalized has size n × n. We then get N/n eigenvalues, each one with degeneracy n, matching the dimensionality of the problem in real space, see e.g. [52].…”

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confidence: 99%

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Topological van Hove singularities at phase transitions in Weyl metals

Fontana,

Burrello,

Trombettoni

2021

Preprint

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We study 3D topological phase transitions between topological and trivial metals and we show that a subset of Van Hove (VH) singularities of the density of states sits exactly at the transition. We may refer to these as topological VH singularities. By investigating a minimal model, we show that they originate from energy saddle points located between Weyl points with opposite chiralities. We exemplify the relation between VH singularities and topological phase transitions in tightbinding Weyl systems by analysing the 3D Hofstadter model, which offers a simple and interesting playground to consider different kinds of Weyl metals and understand the features of their density of states. In this model, as a function the magnetic flux, the occurrence of topological VH singularities can be explicitly checked.

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“…The magnetic field effects are absorbed in the tunneling phases [22] U 1 (r) = 1, U 2 (r) = exp i2πB x − y − 1 2 , and U 3 (r) = exp [−iπB (x − y)] with the cube length a = 1. The phases are obtained under the Hasegawa gauge [23,24] that leads to a translationally invariant Hamiltonian [25][26][27].…”

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confidence: 99%

Magnetic field induced symmetry breaking in nonequilibrium quantum networks

Thingna,

Manzano,

Cao

2019

Preprint

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We study the effect of magnetic field on the nonequilibrium transport properties of a general cubic quantum network described by a tight-binding Hamiltonian. We demonstrate that the symmetry of open systems can be manipulated by the direction of the magnetic field. Starting with all the symmetries preserved in absence of a field, the anisotropic and isotropic field systematically break the symmetries, influencing all nonequilibrium properties. For square and cubic structure, we are able to identify the steady states that comprise of pure states, bath-dependent states (nonequilibrium steady states), and also nonphysical states. As an application, we show numerically for large cubic networks that the symmetry breaking can control nonequilibrium currents and that different environmental interactions can lead to novel features which can be engineered in artificial super-lattices and cold atoms.

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Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials

Cited by 8 publications

References 73 publications

Synthesis of Majorana mass terms in low-energy quantum systems

Synthesis of Majorana mass terms in low-energy quantum systems

Topological van Hove singularities at phase transitions in Weyl metals

Magnetic field induced symmetry breaking in nonequilibrium quantum networks

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