Spectra and Eigenstates of Spin Chain Hamiltonians

Energy Spectra and Eigenstates of Quasiperiodic Tight–Binding Hamiltonians

0 . 1 Energy spectra and eigenstates of quasiperiodic tight - binding Hamiltonians

Among the physical properties of quasicrystals [1], their transport properties, such as the electric conductivity, have attracted particular attention. Over the past decades, a lot of experimental and theoretical effort has been spent on the investigation and explanation of transport anomalies in quasicrystals, see [2, 3, 4] for recent collections of review articles and [5] for further referenc...

Spin Chain Hamiltonians with Affine U q g symmetry

We construct the family of spin chain Hamiltonians, which have affine U q g guantum group symmetry. Their eigenvalues coincides with the eigenvalues of the usual spin chain Hamiltonians which have non-affine U q g 0 quantum group symmetry, but have the degeneracy of levels, corresponding to affine U q g. The space of states of these chaines are formed by the tensor product of the fully reducibl...

Improved Techniques for Preparing Eigenstates of Fermionic Hamiltonians

Dominic W. Berry, Mária Kieferová, 2 Artur Scherer, Yuval R. Sanders, Guang Hao Low, Nathan Wiebe, Craig Gidney, and Ryan Babbush ∗ Department of Physics and Astronomy, Macquarie University, Sydney, NSW 2109, Australia Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada Microsoft Research, Redmond, WA 98052, United States...

Discrete Spectra of Semirelativistic Hamiltonians

We review various attempts to localize the discrete spectra of semirelativistic Hamiltonians of the form H = β √ m2 + p2+V (r) (defined, without loss of generality but for definiteness, in three spatial dimensions) as entering, for instance, in the spinless Salpeter equation; every Hamiltonian in this class of operators consists of the relativistic kinetic energy β √ m2 + p2, where β > 0 allows...