Mesoscopic quantum systems exhibit complex manybody quantum phenomena, where interactions between spins and charges give rise to collective modes and topological states. Even simple, noninteracting theories display a rich landscape of energy states—distinct manyparticle configurations connected by spin and energydependent transition rates. The ways in which these energy states interact is difficult to characterize or predict, especially in regimes of frustration where manybody effects create a multiply degenerate landscape. Here, we use network science to characterize the complex interconnection patterns of these energystate transitions. Using an experimentally verified computational model of electronic transport through quantum antidots, we construct networks where nodes represent accessible energy states and edges represent allowed transitions. We find that these networks exhibit Rentian scaling, which is characteristic of efficient transportation systems in computer circuitry, neural circuitry, and human mobility, and can be used to measure the interconnection complexity of a network. We find that the topological complexity of the state transition networks—as measured by Rent’s exponent— correlates with the amount of current flowing through the antidot system. Furthermore, networks corresponding to points of frustration (due, for example, to spinblockade effects) exhibit an enhanced topological complexity relative to nonfrustrated networks. Our results demonstrate that network characterizationsmore »
This content will become publicly available on January 7, 2023
 Award ID(s):
 2011386
 Publication Date:
 NSFPAR ID:
 10330474
 Journal Name:
 Journal of Physics: Condensed Matter
 Volume:
 34
 Issue:
 12
 Page Range or eLocationID:
 125802
 ISSN:
 09538984
 Sponsoring Org:
 National Science Foundation
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