Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session T00: Poster Session III (1pm-4pm PST)
1:00 PM,
Thursday, March 9, 2023
Room: Exhibit Hall (Forum Ballroom)
Sponsoring
Unit:
APS
Abstract: T00.00113 : Computing the Many Body Density of States of a system of non interacting identical quantum particles*
Presenter:
Rémi Lefèvre
(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)
requires one to go beyond the low-energy physics and local or few body Densities of States (DoS).
MB localization, thermalization (or lack of) and quantum chaos are phenomena in which states at
various energy scales contribute to the dynamics. Enumerating these states with a many-body DoS
is a crucial step in order to build a statistical description of systems displaying such phenomena.
Surprisingly, such a calculation, which dates back to H. Bethe [1], has proved to be very difficult
even in the non interacting case [2].
We provide in this work an exact analytic method based on a principal component analysis which
characterize universal properties of a fermonic MB spectrum. This is done by decoupling the
combinatoric information inherent to a set of MB configurations, from any particular choice of the
single-body spectrum with given number of states and particles.
The method can account for symmetries and the associated conserved quantities, and can be extended
to bosons. We give applications to simple models such as tight-binding and transverse Ising chains.
Exact and fast numerical computations can be made for large systems since the time-consuming part
is universal and can be re-used for all MB systems of a given size [3].
[1] H. Bethe, Phy. Rev. (1936)
[2] V. Zelevinsky and M. Horoi, Progress in Particle and Nuclear Physics (2018)
[3] R. Lefevre, K. deZawadzki and G. Ithier, arXiv:2208.02236
*We acknowledge funding from the Leverhulme Trust under grant RPG-2020-094
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