Shivaji Lal Sondhi

TL;DR: In this article, the performance of the quantum adiabatic algorithm for the solution of decision problems is investigated and the possible failure mechanisms are divided into two sets: small gaps due to quantum phase transitions and small gaps caused by avoided crossings inside a phase.

TL;DR: In this paper, the authors describe an experimental identification and characterization of a new low temperature transport regime near the quantum Hall-to-insulator transition, where a wide range of transport data are compactly described by a simple phenomenological form which is inconsistent with either quantum Hall or insulating behavior and, on the other hand, is also clearly at odds with a quantum critical, or scaling, description.

TL;DR: In this paper, the Hartree-Fock theory is used to provide quantitative estimates of the energies of these excitations and their dependence on Zeeman coupling strength, Landau-level quantum numbers, and the thickness of the two-dimensional electron layers.

TL;DR: In this article, the authors consider two perturbations of the devil's staircase that arise naturally in the experimental setting of cold atomic gases and derive a phase diagram that exhibits this evolution and which supplement by standard wisdom from the Luttinger liquid description of the transitions.

TL;DR: In this article, a family of rotationally invariant, local, $S=1∕2$ Klein Hamiltonians on various lattices that exhibit ground-state manifolds spanned by nearest-neighbor valence bond states was constructed.