We analyse the phase diagram of ultra-cold bosons in a one-dimensional superlattice potential with disorder using the time evolving block decimation algorithm for infinite sized systems (iTEBD). For degenerate potential energies within the unit cell of the superlattice loophole-shaped insulating phases with non-integer filling emerge with a particle-hole gap proportional to the boson hopping. Adding a small amount of disorder destroys this gap. For not too large disorder the loophole Mott regions detach from the axis of vanishing hopping giving rise to insulating islands. Thus the system shows a transition from a compressible Bose-glass to a Mott-insulating phase with increasing hopping amplitude. We present a straight forward effective model for the dynamics within a unit cell which provides a simple explanation for the emergence of Mott-insulating islands. In particular it gives rather accurate predictions for the inner critical point of the Bose-glass to Mott-insulator transition.
We elucidate the mechanism by which a Mott insulator transforms into a non-Fermi liquid metal upon increasing disorder at half filling. By correlating maps of the local density of states, the local magnetization and the local bond conductivity, we find a collapse of the Mott gap toward a V-shape pseudogapped density of states that occurs concomitantly with the decrease of magnetism around the highly disordered sites but an increase of bond conductivity. These metallic regions percolate to form an emergent non-Fermi liquid phase with a conductivity that increases with temperature. Bond conductivity measured via local microwave impedance combined with charge and spin local spectroscopies are ideal tools to corroborate our predictions.
The topological Anderson and Mott insulators are two phases that have so far been separately and widely explored beyond topological band insulators. Here we combine the two seemingly different topological phases into a system of spin-1/2 interacting fermionic atoms in a disordered optical lattice. We find that the topological Anderson and Mott insulators in the noninteracting and clean limits can be adiabatically connected without gap closing in the phase diagram of our model. Lying between the two phases, we uncover a disordered correlated topological insulator, which is induced from a trivial band insulator by the combination of disorder and interaction, as the generalization of topological Anderson insulators to the many-body interacting regime. The phase diagram is determined by computing various topological properties and confirmed by unsupervised and automated machine learning. We develop an approach to provide a unified and clear description of topological phase transitions driven by interaction and disorder. The topological phases can be detected from disorder/interaction induced edge excitations and charge pumping in optical lattices.
Bosons in a periodic lattice with on-site disorder at low but non-zero temperature are considered within a mean-field theory. The criteria used for the definition of the superfluid, Mott insulator and Bose glass are analysed. Since the compressibility does never vanish at non-zero temperature, it can not be used as a general criterium. We show that the phases are unambiguously distinguished by the superfluid density and the density of states of the low-energy exitations. The phase diagram of the system is calculated. It is shown that even a tiny temperature leads to a significant shift of the boundary between the Bose glass and superfluid.
Even though no local order parameter in the sense of the Landau theory exists for topological quantum phase transitions in Chern insulators, the highly non-local Berry curvature exhibits critical behavior near a quantum critical point. We investigate the critical properties of its real space analog, the local Chern marker, in weakly disordered Chern insulators. Due to disorder, inhomogeneities appear in the spatial distribution of the local Chern marker. Their size exhibits power-law scaling with the critical exponent matching the one extracted from the Berry curvature of a clean system. We drive the system slowly through such a quantum phase transition. The characteristic size of inhomogeneities in the non-equilibrium post-quench state obeys the Kibble-Zurek scaling. In this setting, the local Chern marker thus does behave in a similar way as a local order parameter for a symmetry breaking second order phase transition. The Kibble-Zurek scaling also holds for the inhomogeneities in the spatial distribution of excitations and of the orbital polarization.
We study charge transport in one-dimensional graphene superlattices created by applying layered periodic and disordered potentials. It is shown that the transport and spectral properties of such structures are strongly anisotropic. In the direction perpendicular to the layers, the eigenstates in a disordered sample are delocalized for all energies and provide a minimal non-zero conductivity, which cannot be destroyed by disorder, no matter how strong this is. However, along with extended states, there exist discrete sets of angles and energies with exponentially localized eigenfunctions (disorder-induced resonances). It is shown that, depending on the type of the unperturbed system, the disorder could either suppress or enhance the transmission. Most remarkable properties of the transmission have been found in graphene systems built of alternating p-n and n-p junctions. This transmission has anomalously narrow angular spectrum and, surprisingly, in some range of directions it is practically independent of the amplitude of fluctuations of the potential. Owing to these features, such samples could be used as building blocks in tunable electronic circuits. To better understand the physical implications of the results presented here, most of our results have been contrasted with those for analogous wave systems. Along with similarities, a number of quite surprising differences have been found.