Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2009-11-26
Phys. Rev. E 80 (2009) 066706
Physics
Condensed Matter
Statistical Mechanics
12 pages, 10 figures, uses revtex4
Scientific paper
10.1103/PhysRevE.80.066706
In this paper, building on a previous analysis [1] of exact diagonalization of the space-discretized evolution operator for the study of properties of non-relativistic quantum systems, we present a substantial improvement to this method. We apply recently introduced effective action approach for obtaining short-time expansion of the propagator up to very high orders to calculate matrix elements of space-discretized evolution operator. This improves by many orders of magnitude previously used approximations for discretized matrix elements and allows us to numerically obtain large numbers of accurate energy eigenvalues and eigenstates using numerical diagonalization. We illustrate this approach on several one and two-dimensional models. The quality of numerically calculated higher order eigenstates is assessed by comparison with semiclassical cumulative density of states.
Balaz Antun
Belic Aleksandar
Bogojevic Aleksandar
Vidanović Ivana
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