Exploiting the structure of a quantum mechanical Hamiltonian often leads to fast algorithms for computational simulations involving the system. For instance, sparsity of the Hamiltonian can lead to efficient algorithms for obtaining the Green’s function. But can this structure also provide physical insights? In this talk we will discuss the types of structure that can hide in a Hamiltonian by examining the Hamiltonian’s information content. We then apply this idea to two systems. First, we will investigate the complex band structure of an almost-crystalline system, showing that complex band structure is the minimal, intrinsic material information for describing the system . Second, we will tie this hidden Hamiltonian structure to complete destructive interference effects in electron transport through molecules [2, 3].
 M. G. Reuter. J. Phys.: Condens. Matter 29, 053001 (2017).
 M. G. Reuter, T. Hansen. J. Chem. Phys. 141, 181103 (2014).
 P. Sam-ang, M. G. Reuter. New J. Phys. 19, 053002 (2017).