Interactions in Quasicrystals

Abstract

Although the effects of interactions in solid state systems still remains a widely open subject, some limiting cases such as the three dimensional Fermi liquid or the one-dimensional Luttinger liquid are by now well understood when one is dealing with interacting electrons in periodic crystalline structures. This problem is much more fascinating when periodicity is lacking as it is the case in quasicrystalline structures. Here, we discuss the influence of the interactions in quasicrystals and show, on a controlled one-dimensional model, that they lead to anomalous transport properties, intermediate between those of an interacting electron gas in a periodic and in a disordered potential.

Fibonacci optical lattices for tunable quantum quasicrystals

“…The proposed realization of the cut-and-project construction allows tuning across the dimensional crossover from periodic 2D lattices to quasiperiodic 1D chains, enabling direct investigation of descendant quasiperiodic phases of well-studied correlated 2D systems. The unique tools of atomic physics can also enable new types of experiments: Feshbach tuning of the scattering length would allow exploration of the poorly understood role of interactions in quasicrystals [48], and time-varying potentials would enable dynamical experiments impossible in static lattices, such as phason spectroscopy. Experiments on quasiperiodic optical potentials may ultimately prove complementary to synthesis and characterization of solid and photonic quasicrystals, and could open another conceptual angle of attack on the problem of designing and predicting the properties of these complex materials.…”

Fermionic superfluidity and spontaneous superflows in optical lattices

“…The high tunability of the interaction strength between atoms, as well as the easy manipulation of the optical lattices makes the system realistically viable to implement a quantum simulator [4]. The quantum atomic gases in optical lattices make it possible to build a model system so that we can explore the correlated properties in many-body physics such as superconductivity, quantum magnetism, quantum criticality, etc, and examine the related theoretical models [5][6][7].…”

Tunneling into a Finite Luttinger Liquid Coupled to Noisy Capacitive Leads

“…Interacting wires are better described using Tomonaga-Luttinger liquid (TLL) theory [15][16][17]: the low-energy elementary excitations in 1D appear as collective bosonic plasmon modes -in stark contrast to the constitutive fermionic electrons. Consequently, 1D systems show exotic phenomena, such as charge fractionalization of injected electrons [18,19], spin-charge separation [20,21], and zero-bias anomalies (ZBA) [22][23][24][25], all of which uniquely interplay with disorder [26,27], quasi-disorder [28], and dissipation [29,30]. Such 1D effects are ubiquitous and have been observed in a wide variety of systems, including nanotubes [31,32], GaAs wires [20,21], quantum Hall edges [33][34][35], as well as, chains of spins or atoms [36,37].…”