Generalized quantum Hall projection Hamiltonians

Model Hamiltonians for the Fractional Quantum Hall E ect

The fractional quantum Hall e ect (FQHE), discovered by Stui and Stormer in 1982, has been the subject of much theoretical and experimental interest since. Whereas the integer case (IQHE) can be understood in terms of single-electron behavior in the presence of a magnetic eld, the FQHE appears to be the result of Coulomb interactions between electrons in the system. Laughlin [1] explained the ...

Universal quantum Hamiltonians

Quantum many-body systems exhibit a bewilderingly diverse range of behaviours. Here, we prove that all the physics of every other quantum many-body system is replicated in certain simple, “universal” quantum spin-lattice models. We first characterise precisely and in full generality what it means for one quantum many-body system to replicate the entire physics of another. We then fully classify...

Generalized plasmas and the anomalous quantum Hall effect

Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians.

We show how to numerically calculate several quantities that characterize topological order starting from a microscopic fractional quantum Hall Hamiltonian. To find the set of degenerate ground states, we employ the infinite density matrix renormalization group method based on the matrix-product state representation of fractional quantum Hall states on an infinite cylinder. To study localized q...

Generalized seniority from random Hamiltonians

We investigate the generic pairing properties of shell-model many-body Hamiltonians drawn from ensembles of random two-body matrix elements. Many features of pairing that are commonly attributed to the interaction are in fact seen in a large part of the ensemble space. Not only do the spectra show evidence of pairing with favored J = 0 ground states and an energy gap, but the relationship betwe...