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Locality of the windowed local density of states

Publication ,  Journal Article
Loring, TA; Lu, J; Watson, AB
Published in: Discussion Contributions 10th Vienna Conference on Mathematical Modelling, volume 17. ARGESIM, 2022
January 1, 2021

We introduce a generalization of local density of states which is "windowed" with respect to position and energy, called the windowed local density of states (wLDOS). This definition generalizes the usual LDOS in the sense that the usual LDOS is recovered in the limit where the position window captures individual sites and the energy window is a delta distribution. We prove that the wLDOS is local in the sense that it can be computed up to arbitrarily small error using spatial truncations of the system Hamiltonian. Using this result we prove that the wLDOS is well-defined and computable for infinite systems satisfying some natural assumptions. We finally present numerical computations of the wLDOS at the edge and in the bulk of a "Fibonacci SSH model", a one-dimensional non-periodic model with topological edge states.

Duke Scholars

Published In

Discussion Contributions 10th Vienna Conference on Mathematical Modelling, volume 17. ARGESIM, 2022

Publication Date

January 1, 2021
 

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Loring, T. A., Lu, J., & Watson, A. B. (2021). Locality of the windowed local density of states. Discussion Contributions 10th Vienna Conference on Mathematical  Modelling, Volume 17. ARGESIM, 2022.
Loring, Terry A., Jianfeng Lu, and Alexander B. Watson. “Locality of the windowed local density of states.” Discussion Contributions 10th Vienna Conference on Mathematical  Modelling, Volume 17. ARGESIM, 2022, January 1, 2021.
Loring TA, Lu J, Watson AB. Locality of the windowed local density of states. Discussion Contributions 10th Vienna Conference on Mathematical  Modelling, volume 17 ARGESIM, 2022. 2021 Jan 1;
Loring, Terry A., et al. “Locality of the windowed local density of states.” Discussion Contributions 10th Vienna Conference on Mathematical  Modelling, Volume 17. ARGESIM, 2022, Jan. 2021.
Loring TA, Lu J, Watson AB. Locality of the windowed local density of states. Discussion Contributions 10th Vienna Conference on Mathematical  Modelling, volume 17 ARGESIM, 2022. 2021 Jan 1;

Published In

Discussion Contributions 10th Vienna Conference on Mathematical Modelling, volume 17. ARGESIM, 2022

Publication Date

January 1, 2021