Alleviating finite-size effects in quantum-mechanical systems using magnetic fields

Abstract

It is known that the addition of a single magnetic flux in a finite-sized quantum-mechanical system reduces finite-size effects considerably. In this paper, we quantify this reduction in detail by studying the density of states of a finite-sized system with and without a single magnetic flux. For small system sizes without a magnetic field present, the density of states plot contains multiple jagged regions. However, as one approaches the infinite-system limit, the density of states becomes smoother. Upon adding a magnetic field with unit flux quantum, the density of states plot smoothens and resembles the infinite-system limit even at comparatively small system sizes. In order to quantify the reduction in jaggedness, we generate multiple density of states plots for various system sizes with and without a magnetic flux and use the L² norm similarity metric for comparison between the zero-field and nonzero-field cases.  We find evidence that at least as far as the density of states is concerned, large systems can be mimicked by much smaller ones (even by an order of magnitude) provided one magnetic flux quantum is included.