Comments on the fractal energy spectrum of honeycomb lattice with defects

Matsuki, Yoshiyuki; Ikeda, Kazuki

doi:10.1088/2399-6528/ab18de

Cited by 7 publications

(5 citation statements)

References 25 publications

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“…For further research directions, it will be meaningful to consider the theory with impurities or defects, by which we can address the problems under more realistic conditions. In our recent study [49,50], we showed that the fractal scaling nature of the localized length of the Bloch states localizing around a defect. Studying the localized length can be a powerful method to investigate the fractal nature of the Hofstadter butterfly as well as the energy spectrum.…”

Section: Conclusion and Discussionmentioning

confidence: 93%

Hyperbolic band theory under magnetic field and Dirac cones on a higher genus surface

Ikeda¹,

Aoki²,

Matsuki³

2021

J. Phys.: Condens. Matter

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We explore the hyperbolic band theory under a magnetic field for the first time. Our theory is a general extension of the conventional band theory defined on a Euclidean lattice into the band theory on a general hyperbolic lattice/Riemann surface. Our methods and results can be confirmed experimentally by circuit quantum electrodynamics, which enables us to create novel materials in a hyperbolic space. To investigate the band structures, we construct directly the hyperbolic magnetic Bloch states and find that they form Dirac cones on a coordinate neighborhood. They can be regarded as a global quantum gravity solution detectable in a laboratory. Besides this is the first explicit example of a massless Dirac state on a higher genus surface. Moreover we show that the energy spectrum exhibits an unusual fractal structure refracting the negative curvature, when plotted as a function of a magnetic flux.

show abstract

Section: Conclusion and Discussionmentioning

confidence: 93%

Hyperbolic band theory under magnetic field and Dirac cones on a higher genus surface

Ikeda¹,

Aoki²,

Matsuki³

2021

J. Phys.: Condens. Matter

Self Cite

View full text Add to dashboard Cite

show abstract

“…For further research directions, it will be meaningful to consider the theory with impurities or defects, by which we can address the problems under more realistic conditions. In our recent study [46,47], we showed that the fractal scaling nature of the localized length of the Bloch states localizing around a defect. Studying the localized length can be a powerful method to investigate the fractal nature of the Hofstadter butterfly as well as the energy spectrum.…”

Section: Conclusion and Discussionmentioning

confidence: 93%

Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface

Ikeda,

Aoki,

Matsuki

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We explore the hyperbolic band theory under a magnetic field for the first time. Our theory is a general extension of the conventional band theory defined on a Euclidean lattice into the band theory on a general hyperbolic lattice/Riemann surface. Our methods and results can be confirmed experimentally by circuit quantum electrodynamics (cQED), which enables us to create novel materials in a hyperbolic space. To investigate the band structures, we construct directly the hyperbolic magnetic Bloch states and find that they form Dirac cones on a coordinate neighborhood, by which they can be regarded as a global quantum gravity solution detectable in a laboratory. Besides this is the first explicit example of a massless Dirac state on a higher genus surface. Moreover we show that the energy spectrum exhibits an unusual fractal structure, when plotted as a function of a magnetic flux.

show abstract

“…There are many possible further research directions. For example, it would be a good exercise to simulate dynamics of systems with defects [37]. Moreover in principle, such dynamics can be simulated with a general Ising model with XX interactions.…”

Section: Discussionmentioning

confidence: 99%

Universal Computation with Quantum Fields

Ikeda

2019

Preprint

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We explore a way of universal quantum computation with particles which cannot occupy the same position simultaneously and are symmetric under exchange of particle labels. Therefore the associated creation and annihilation operators are neither bosonic nor fermionic. In this work we first show universality of our method and numerically address several examples. We demonstrate dynamics of a Bloch electron system from a viewpoint of adiabatic quantum computation. In addition we provide a novel Majorana fermion system and analyze phase transitions with spin-coherent states and the time average of the OTOC (out-of-time-order correlator). We report that a first-order phase transition is avoided when it evolves in a non-stoquastic manner and the time average of the OTOC diagnoses the phase transitions successfully.

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Comments on the fractal energy spectrum of honeycomb lattice with defects

Cited by 7 publications

References 25 publications

Hyperbolic band theory under magnetic field and Dirac cones on a higher genus surface

Hyperbolic band theory under magnetic field and Dirac cones on a higher genus surface

Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface

Universal Computation with Quantum Fields

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