Securitisation

Graf, Georg; Hinteregger, Monika; Weissenbacher, Manuela; Allemeersch, Benoit; Verbeke, Alain Laurent; Clausen, Merete; Smith, Lionel; Tuomisto, Jarmo; Barrière, François; Grundmann, Stefan; Lekkas, George K.; Moloney, Niamh; O'Dell, Eoin; Gambaro, Antonio; Graziadei, Michele; Jacoby, Steve; Koppenol-Laforce, Marielle; Vasconcelos, Pedro Pais de; Gretton, George; Lapuente, Sergio Cámara; Beilfuss, Cristina González; Håstad, Torgny

doi:10.1017/cbo9780511494956.017

Cited by 1 publication

(1 citation statement)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the bound is not good enough to determine σ uniquely. A colored Hofstadter butterfly for the hexagonal model has been made in the diploma thesis of Andrea Agazzi [11] where the Chern numbers were numerically computed using edge currents. This approach is numerically intensive.…”

Section: )mentioning

confidence: 99%

A study of the ambiguity in the solutions to the Diophantine equation for Chern numbers

Avron¹,

Kenneth²,

Yehoshua³

2014

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

The Chern numbers for Hofstadter models with rational flux 2πp/q are partially determined by a Diophantine equation. A M od q ambiguity remains. The resolution of this ambiguity is only known for the rectangular lattice with nearest neighbors hopping where it has the form of a "window condition". We study a Hofstadter butterfly on the triangular lattice for which the resolution of ambiguity is open. In the model many pairs (p, q) satisfy a window condition which is shifted relative to the window of the square model. However, we also find pairs (p, q) where the Chern numbers do not belong to any contiguous window. This shows that the rectangular model and the one we study on the triangular lattice are not adiabatically connected: Many gaps must close. Our results suggest the conjecture that the mod q ambiguity in the Diophantine equation generically reduces to a sign ambiguity.1 The phase diagrams we consider should be distinguished from phase diagrams which describe the localization properties and the Liapunov exponent described e.g. in [12].

show abstract

Section: )mentioning

confidence: 99%