Non-Local Finite-Size Effects in the Dimer Model

We study the finite-size corrections of the dimer model on $\infty \times N$ square lattice with two different boundary conditions: free and periodic. We find that the finite-size corrections depend in a crucial way on the parity of $N$, and show that, because of certain non-local features present in the model, a change of parity of $N$ induces a change of boundary condition. Taking a careful account of this, these unusual finite-size behaviours can be fully explained in the framework of the $c=-2$ logarithmic conformal field theory.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

A universal conformal field theory approach to the chiral persistent currents in the mesoscopic fractional quantum Hall states

We propose a general and compact scheme for the computation of the periods and amplitudes of the chiral persistent currents, magnetizations and magnetic susceptibilities in mesoscopic fractional quantum Hall disk samples threaded by Aharonov--Bohm magnetic field. This universal approach uses the effective conformal field theory for the edge states in the quantum Hall effect to derive explicit formulas for the corresponding partition functions in presence of flux. We point out the crucial role of a special invariance condition for the partition function, following from the Bloch-Byers-Yang theorem, which represents the Laughlin spectral flow. As an example we apply this procedure to the Z_k parafermion Hall states and show that they have universal non-Fermi liquid behavior without anomalous oscillations. For the analysis of the high-temperature asymptotics of the persistent currents in the parafermion states we derive the modular S-matrices constructed from the S matrices for the u(1) sector and that for the neutral parafermion sector which is realized as a diagonal affine coset.Comment: 45 pages, LaTeX2e, 4 EPS figures, 1 table, for related color figures see http://theo.inrne.bas.bg/~lgeorg/PF_k.htm

Loop quantization from a lattice gauge theory perspective

We present an interpretation of loop quantization in the framework of lattice gauge theory. Within this context the lack of appropriate notions of effective theories and renormalization group flow exhibit loop quantization as an incomplete framework. This interpretation includes a construction of embedded spin foam models which does not rely on the choice of any auxiliary structure (e.g. triangulation) and has the following straightforward consequences: (1) The values of the coupling constants need to be those of an UV-attractive fixed point (2) The kinematics of canonical loop quantization and embedded spin foam models are compatible (3) The weights assigned to embedded spin foams are independent of the 2-polyhedron used to regularize the path integral, $|J|_x = |J|_{x'}$ (4) An area spectrum with edge contributions proportional to $l_{\rm PL}^2 (j+1 / 2)$ is not compatible with embedded spin foam models and/or canonical loop quantizationComment: 11 pages, no figures; completely rewritte

Entanglement properties of spin models in triangular lattices

The different quantum phases appearing in strongly correlated systems as well as their transitions are closely related to the entanglement shared between their constituents. In 1D systems, it is well established that the entanglement spectrum is linked to the symmetries that protect the different quantum phases. This relation extends even further at the phase transitions where a direct link associates the entanglement spectrum to the conformal field theory describing the former. For 2D systems much less is known. The lattice geometry becomes a crucial aspect to consider when studying entanglement and phase transitions. Here, we analyze the entanglement properties of triangular spin lattice models by considering also concepts borrowed from quantum information theory such as geometric entanglement.Comment: 19 pages, 8 figure