Bulletin of the American Physical Society
2023 APS March Meeting
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session B33: Quantum Quenches and Integrability
11:30 AM–1:54 PM,
Monday, March 6, 2023
Room: Room 225
Sponsoring
Unit:
DCMP
Chair: Ke Wang, University of Chicago
Abstract: B33.00007 : Many Body Density of States of a system of non interacting fermions*
12:42 PM–12:54 PM
Presenter:
Gregoire Ithier
(Royal Holloway University of London)
Authors:
Gregoire Ithier
(Royal Holloway University of London)
Rémi Lefèvre
(Royal Holloway University of London)
Krissia d Zawadzki
(Trinity College Dublin)
It is only recently, with the progress in quantum engineering and simulation, that the necessity to calculate Many Body densities of states has came back to light. For instance, a phenomenon like Many Body Localization requires to go beyond the low energy physics and consider excitations from the full energy range of the system spectrum [3,4]. More generally, closed quantum systems exhibiting unconventional stationary states require to enumerate the number of accessible states in order to build their statistical description. Such an enumeration requires the MBDoS whose calculation is challenging due to the difficulty in counting states while enforcing the exchange symmetry [4].
In the present work, we introduce a new approach for calculating the MBDoS of systems of non interacting fermions. The starting point of our method is the principal component analysis of a filling matrix F describing how N fermions can be configured into K single-particle energy levels. We show that the many body spectrum can be expanded as a weighted sum of universal spectra given by the principal components of the filling matrix. The weighting coefficients involve renormalized energies obtained from the single body spectrum and indicate which components dominate the spectral behavior of the system under consideration [5].
By considering each principal spectrum and their degeneracies, one can classify non interacting many body states and quantify how they will be affected by a subsequent interaction, depending if this interaction is single, two or generally, k-body like. We illustrate the potential of our method on the Anderson localization problem.
[1] H. Bethe, Phys. Rev., (1936)
[2] Schreiber et al, Science, (2015)
[3] Gross et al, Science (2017)
[4] V. Zelevinsky and M. Horoi, Prog. in Part. And Nucl. Phys. (2018)
[5] R. Lefevre et al, arXiv:2208.02236
*We acknowledge support from the Leverhulme Trust under grant RPG-2020-094
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