Strong correlations at topological insulator surfaces and the breakdown of the bulk-boundary correspondence

The criteria for strong correlations on surfaces of three-dimensional topological insulators are discussed. Usually, the Coulomb repulsion at such surfaces is too weak for driving a phase transition to a strongly correlated regime. I discuss a mechanism and possibilities of its experimental implementation by which the strength of the Coulomb interaction can be tuned over a wide range. In the strongly interacting regime, the surface states are gapped, even though the topological classification of the bulk band structure predicts gapless surface states

Bosonic field theory of tunable edge magnetism in graphene

A bosonic field theory is derived for the tunable edge magnetism at graphene zigzag edges. The derivation starts from an effective fermionic theory for the interacting graphene edge states, derived previously from a two-dimensional interacting tight-binding model for graphene. The essential feature of this effective model, which gives rise to the weak edge magnetism, is the momentum-dependent non-local electron-electron interaction. It is shown that this momentum-dependence may be treated by an extension of the bosonization technique, and leads to interactions of the bosonic fields. These interactions are reminiscent of a \phi^4 field theory. Focussing onto the regime close to the quantum phase transition between the ferromagnetic and the paramagnetic Luttinger liquid, a semiclassical interpretation of the interacting bosonic theory is given. Furthermore, it is argued that the universal critical behavior at the quantum phase transition between the paramagnetic and the ferromagnetic Luttinger liquid is governed by a small number of terms in this theory, which are accessible by quantum Monte-Carlo methods

BTZ Black Hole Entropy in Loop Quantum Gravity and in Spin Foam Models

We present a comparison of the calculation of BTZ black hole entropy in loop quantum gravity and in spin foam models. We see that both give the same answer.Comment: 10 pages, 3 figures, Final version, improve

Black Hole Entropy in Loop Quantum Gravity and Number Theory

We show that counting different configurations that give rise to black hole entropy in loop quantum gravity is related to partitions in number theory.Comment: 6 page

Entropy in Spin Foam Models: The Statistical Calculation

Recently an idea for computing the entropy of black holes in the spin foam formalism has been introduced. Particularly complete calculations for the three dimensional euclidean BTZ black hole were done. The whole calculation is based on observables living at the horizon of the black hole universe. Departing from this idea of observables living at the horizon, we now go further and compute the entropy of BTZ black hole in the spirit of statistical mechanics. We compare both calculations and show that they are very interrelated and equally valid. This latter behaviour is certainly due to the importance of the observables.Comment: 11 pages, 1 figur