When is an area law not an area law?

Entanglement entropy is typically proportional to area, but sometimes it acquires an additional logarithmic pre-factor. We offer some intuitive explanations for these facts.Comment: plainTeX, 12 pages, 3 figures. A more current version may be available at http://www.perimeterinstitute.ca/personal/rsorkin/some.papers

Topological phases and quantum computation

This is a collection of lecture notes from three lectures given by Alexei Kitaev at the 2008 Les Houches summer school "Exact methods in low-dimensional physics and quantum computing." They provide a pedagogical introduction to topological phenomena in 1-D superconductors and in the 2-D topological phases of the toric code and honeycomb model.Comment: 31 pages. Lectures given by Alexei Kitaev at the 2008 Les Houches Summer School "Exact methods in low-dimensional physics and quantum computing

SU(2)-invariant spin liquids on the triangular lattice with spinful Majorana excitations

We describe a new class of spin liquids with global SU(2) spin rotation symmetry in spin 1/2 systems on the triangular lattice, which have real Majorana fermion excitations carrying spin S = 1. The simplest translationally-invariant mean-field state on the triangular lattice breaks time-reversal symmetry and is stable to fluctuations. It generically possesses gapless excitations along 3 Fermi lines in the Brillouin zone. These intersect at a single point where the excitations scale with a dynamic exponent z = 3. An external magnetic field has no orbital coupling to the SU(2) spin rotation-invariant fermion bilinears that can give rise to a transverse thermal conductivity, thus leading to the absence of a thermal Hall effect. The Zeeman coupling is found to gap out two-thirds of the z = 3 excitations near the intersection point and this leads to a suppression of the low temperature specific heat, the spin susceptibility and the Wilson ratio. We also compute physical properties in the presence of weak disorder and discuss possible connections to recent experiments on organic insulators.Comment: 26 pages, 11 figure

Many-body mobility edge due to symmetry-constrained dynamics and strong interactions

We provide numerical evidence combined with an analytical understanding of the many-body mobility edge for the strongly anisotropic spin-1/2 XXZ model in a random magnetic field. The system dynamics can be understood in terms of symmetry-constrained excitations about parent states with ferromagnetic and anti-ferromagnetic short range order. These two regimes yield vastly different dynamics producing an observable, tunable many-body mobility edge. We compute a set of diagnostic quantities that verify the presence of the mobility edge and discuss how weakly correlated disorder can tune the mobility edge further.Comment: 10 pages, 5 figure

Long-range quantum gates using dipolar crystals

We propose the use of dipolar spin chains to enable long-range quantum logic between distant qubits. In our approach, an effective interaction between remote qubits is achieved by adiabatically following the ground state of the dipolar chain across the paramagnet to crystal phase transition. We demonstrate that the proposed quantum gate is particularly robust against disorder and derive scaling relations, showing that high-fidelity qubit coupling is possible in the presence of realistic imperfections. Possible experimental implementations in systems ranging from ultracold Rydberg atoms to arrays of Nitrogen-Vacancy defect centers in diamond are discussed.Comment: 5 pages, 3 figure

Hybrid Dyons, inverted Lorentz force and magnetic Nernst effect in quantum spin ice

Topological magnets host two sets of gauge fields: that of native Maxwell electromagnetism, thanks to the magnetic dipole moment of its constituent microscopic moments; and that of the emergent gauge theory describing the topological phase. Here, we show that in quantum spin ice, the emergent magnetic charges of the latter carry native electric charge of the former. We both provide a general symmetry-based analysis underpinning this result, and discuss a microscopic mechanism which binds a native electric charge to the emergent magnetic one. This has important ramifications. First and foremost, an applied electric field gives rise to an emergent magnetic field. This in turn exerts an `inverted' Lorentz force on moving emergent electric/native magnetic charges. This can be probed via what we term a magnetic Nernst effect: applying an electric field perpendicular to a temperature gradient yields a magnetisation perpendicular to both. Finally, and importantly as a further potential experimental signature, a thermal gas of emergent magnetic charges will make an activated contribution to the optical conductivity at low temperatures.Comment: 11 pages, 2 figure