High-temperature expansion for Ising models on quasiperiodic tilings

We consider high-temperature expansions for the free energy of zero-field Ising models on planar quasiperiodic graphs. For the Penrose and the octagonal Ammann-Beenker tiling, we compute the expansion coefficients up to 18th order. As a by-product, we obtain exact vertex-averaged numbers of self-avoiding polygons on these quasiperiodic graphs. In addition, we analyze periodic approximants by computing the partition function via the Kac-Ward determinant. For the critical properties, we find complete agreement with the commonly accepted conjecture that the models under consideration belong to the same universality class as those on periodic two-dimensional lattices.Comment: 24 pages, 8 figures (EPS), uses IOP styles (included

Artificial graphene as a tunable Dirac material

Artificial honeycomb lattices offer a tunable platform to study massless Dirac quasiparticles and their topological and correlated phases. Here we review recent progress in the design and fabrication of such synthetic structures focusing on nanopatterning of two-dimensional electron gases in semiconductors, molecule-by-molecule assembly by scanning probe methods, and optical trapping of ultracold atoms in crystals of light. We also discuss photonic crystals with Dirac cone dispersion and topologically protected edge states. We emphasize how the interplay between single-particle band structure engineering and cooperative effects leads to spectacular manifestations in tunneling and optical spectroscopies.Comment: Review article, 14 pages, 5 figures, 112 Reference

Fidelity susceptibility in the two-dimensional spin-orbit models

We study the quantum phase transitions in the two-dimensional spin-orbit models in terms of fidelity susceptibility and reduced fidelity susceptibility. An order-to-order phase transition is identified by fidelity susceptibility in the two-dimensional Heisenberg XXZ model with Dzyaloshinsky-Moriya interaction on a square lattice. The finite size scaling of fidelity susceptibility shows a power-law divergence at criticality, which indicates the quantum phase transition is of second order. Two distinct types of quantum phase transitions are witnessed by fidelity susceptibility in Kitaev-Heisenberg model on a hexagonal lattice. We exploit the symmetry of two-dimensional quantum compass model, and obtain a simple analytic expression of reduced fidelity susceptibility. Compared with the derivative of ground-state energy, the fidelity susceptibility is a bit more sensitive to phase transition. The violation of power-law behavior for the scaling of reduced fidelity susceptibility at criticality suggests that the quantum phase transition belongs to a first-order transition. We conclude that fidelity susceptibility and reduced fidelity susceptibility show great advantage to characterize diverse quantum phase transitions in spin-orbit models.Comment: 11 pages. 11 figure

Bethe Ansatz solution of triangular trimers on the triangular lattice

Details are presented of a recently announced exact solution of a model consisting of triangular trimers covering the triangular lattice. The solution involves a coordinate Bethe Ansatz with two kinds of particles. It is similar to that of the square-triangle random tiling model, due to M. Widom and P. A. Kalugin. The connection of the trimer model with related solvable models is discussed.Comment: 33 pages, LaTeX2e, 13 EPS figures, PSFra

Lattice dependence of saturated ferromagnetism in the Hubbard model

We investigate the instability of the saturated ferromagnetic ground state (Nagaoka state) in the Hubbard model on various lattices in dimensions d=2 and d=3. A variational resolvent approach is developed for the Nagaoka instability both for U = infinity and for U < infinity which can easily be evaluated in the thermodynamic limit on all common lattices. Our results significantly improve former variational bounds for a possible Nagaoka regime in the ground state phase diagram of the Hubbard model. We show that a pronounced particle-hole asymmetry in the density of states and a diverging density of states at the lower band edge are the most important features in order to stabilize Nagaoka ferromagnetism, particularly in the low density limit.Comment: Revtex, 18 pages with 18 figures, 7 pages appendices, section on bcc lattice adde

Quasicrystalline Order in Binary Dipolar Systems

Motivated by recent experimental findings, we investigate the possible occurrence and characteristics of quasicrystalline order in two-dimensional mixtures of point dipoles with two sorts of dipole moments. Despite the fact that the dipolar interaction potential does not exhibit an intrinsic length scale and cannot be tuned a priori to support the formation of quasicrystalline order, we find that configurations with long--range quasicrystallinity yield minima in the potential energy surface of the many particle system. These configurations emanate from an ideal or perturbed ideal decoration of a binary tiling by steepest descent relaxation. Ground state energy calculations of alternative ordered states and parallel tempering Monte-Carlo simulations reveal that the quasicrystalline configurations do not correspond to a thermodynamically stable state. On the other hand, steepest descent relaxations and conventional Monte-Carlo simulations suggest that they are rather robust against fluctuations. Local quasicrystalline order in the disordered equilibrium states can be strong.Comment: 10 pages, 7 figure