Particle Creation at a Point Source by Means of Interior-Boundary Conditions

We consider a way of defining quantum Hamiltonians involving particle creation and annihilation based on an interior-boundary condition (IBC) on the wave function, where the wave function is the particle-position representation of a vector in Fock space, and the IBC relates (essentially) the values of the wave function at any two configurations that differ only by the creation of a particle. Here we prove, for a model of particle creation at one or more point sources using the Laplace operator as the free Hamiltonian, that a Hamiltonian can indeed be rigorously defined in this way without the need for any ultraviolet regularization, and that it is self-adjoint. We prove further that introducing an ultraviolet cut-off (thus smearing out particles over a positive radius) and applying a certain known renormalization procedure (taking the limit of removing the cut-off while subtracting a constant that tends to infinity) yields, up to addition of a finite constant, the Hamiltonian defined by the IBC.Comment: 41 page

Unconventional magnets in external magnetic fields

This short review surveys phenomena observed when a magnetic field is applied to a system of localised spins on a lattice. Its focus is on frustrated magnets in dimension $d \geq 2$. The interplay of field and entropy is illustrated in the context of their unusual magnetocaloric properties, where field-tuned degeneracies assert themselves. Magnetisation plateaux can reveal the physics of fluctuations, with unusual excitations (such as local modes, extended string defects or monopoles) involved in plateau termination. Field-tuning lattice geometry is the final topic, where mechanisms for dimensional reduction and conversion between different lattice types are discussed.Comment: Plenary Talk at HFM 2008 Conferenc

Linear independence of localized magnon states

At the magnetic saturation field, certain frustrated lattices have a class of states known as "localized multi-magnon states" as exact ground states. The number of these states scales exponentially with the number $N$ of spins and hence they have a finite entropy also in the thermodynamic limit $N\to \infty$ provided they are sufficiently linearly independent. In this article we present rigorous results concerning the linear dependence or independence of localized magnon states and investigate special examples. For large classes of spin lattices including what we called the orthogonal type and the isolated type as well as the kagom\'{e}, the checkerboard and the star lattice we have proven linear independence of all localized multi-magnon states. On the other hand the pyrochlore lattice provides an example of a spin lattice having localized multi-magnon states with considerable linear dependence.Comment: 23 pages, 6 figure