Renormalization, freezing phase transitions and Fibonacci quasicrystals

Renormalization, Freezing Phase Transitions and Fibonacci Quasicrystals

We examine the renormalization operator determined by the Fibonacci substitution. We exhibit a fixed point and determine its stable leaf (under iteration of the operator). Then, we study the thermodynamic formalism for potentials in this stable leaf, and prove they have a freezing phase transition, with ground state supported on the attracting quasi-crystal associated to the Fibonacci substitut...

Environmentally Friendly Renormalization Group and Phase Transitions

We discuss an environmentally friendly renormalization group approach to analyze phase transitions. We intend to apply this method to the Electroweak Phase Transition. This work is in progress. We present some previously obtained results concerning a λφ 4 theory, where the main features of this algorithm are introduced.

Observation of topological phase transitions in photonic quasicrystals.

Topological insulators and topological superconductors are distinguished by their bulk phase transitions and gapless states at a sharp boundary with the vacuum. Quasicrystals have recently been found to be topologically nontrivial. In quasicrystals, the bulk phase transitions occur in the same manner as standard topological materials, but their boundary phenomena are more subtle. In this Letter...

Fibonacci Optical Lattices for Tunable Quantum Quasicrystals

We describe a new type of quasiperiodic optical lattice, created by a physical realization of the abstract cut-and-project construction underlying all quasicrystals. The resulting potential is a generalization of the Fibonacci tiling. Calculation of the energies and wavefunctions of ultracold atoms loaded into such a lattice demonstrate a multifractal energy spectrum, a singular continuous mome...

Fibonacci Fixed Point of Renormalization