We study a one-dimensional Fermi gas with attractive short range-interactions in a disordered potential by the density matrix renormalization group (DMRG) technique. Our results can be tested experimentally by using cold atom techniques. We identify a region of parameters for which disorder enhances the superfluid state. As disorder is further increased, global superfluidity eventually breaks down. However this transition seems to occur before the transition to the insulator state takes place. This suggests the existence of an intermediate metallic ``pseudogap'' phase characterized by strong pairing but no quasi-long-range order.
We study the effects of electron-electron interactions in disordered metals in and close to two dimensions (2D). We consider physical situations in which localization effects are suppressed. The field-theoretical renormalization-group (RG) calculation performed recently by Finkelstein is interpreted and rederived in terms of perturbative results. Surprisingly, except for the density of states, the scaling behavior is independent of the interaction range. We further extend the model to several new universality classes. In the presence of a strong magnetic field the metal is unstable in 2D and undergoes a metal-insulator transition in $d=2+\ensuremath{\epsilon}$. The conductivity exponent, defined by $\ensuremath{\sigma}\ensuremath{\sim}{(n\ensuremath{-}{n}_{c})}^{\ensuremath{\mu}}$, is universal with $\ensuremath{\mu}=1+O(\ensuremath{\epsilon})$ but
N(EF) depends not only on the range of the interaction but also on its strength for short-ranged interactions. In 2D the conductivity has a universal temperature dependence [$\ensuremath{\delta}\ensuremath{\sigma}(T)={\ensuremath{\sigma}}_{N}(2\ensuremath{-}2\mathrm{ln}2)\mathrm{ln}(T\ensuremath{\tau})$, ${\ensuremath{\sigma}}_{N}=\frac{{e}^{2}}{2{\ensuremath{\pi}}^{2}\ensuremath{\hbar}}$] if the interaction is Coulombic. If magnetic impurities (or strong spin-orbit scattering with a weak magnetic field) are present instead, the noninteracting fixed point is stable for short-ranged interactions ($\ensuremath{\mu}=\frac{1}{2}$). For the Coulomb interaction the interaction is relevant and drives a metal-insulator transition in $d=2+\ensuremath{\epsilon}$ with universal critical properties ($\ensuremath{\mu}=1$). In 2D the conductivity also has a universal temperature dependence [$\ensuremath{\delta}\ensuremath{\sigma}(T)={\ensuremath{\sigma}}_{N}\mathrm{ln}(T\ensuremath{\tau})$]. We also discuss the behavior of the dielectric constant on the insulator side and the frequency (temperature) dependence of the conductivity at criticality. Remarks are made on the relationship of the above to experiments.
Understanding the interplay of interaction and disorder in quantum transport poses long-standing scientific challenges for theory and experiment. While highly controlled ultracold atomic platforms combining atomic interactions with spatially disordered lattices have led to remarkable advances, the extension of such controlled studies to phenomena in high-dimensional disordered systems, such as the three-dimensional Anderson metal-insulator transition has been limited. Kicked quantum gases provide an alternate experimental platform that captures the Anderson model in momentum space and features dynamical localization as the analog of Anderson localization. Here, we utilize a momentum space lattice platform using quasiperiodically kicked ultracold atomic gases to experimentally investigate interaction effects on the three-dimensional dynamical Anderson metal-insulator transition. We observe interaction-driven subdiffusion and a divergence of delocalization onset time on approaching the phase boundary. Mean-field numerical simulations show qualitative agreement with experimental observations, but with significant quantitative deviations.
We investigate the zero-temperature metal-insulator transition in a one-dimensional two-component Fermi gas in the presence of a quasiperiodic potential resulting from the superposition of two optical lattices of equal intensity but incommensurate periods. A mobility edge separating (low-energy) Anderson localized and (high-energy) extended single-particle states appears in this continuous-space model beyond a critical intensity of the quasiperiodic potential. To discern the metallic phase from the insulating phase in the interacting many-fermion system, we employ unbiased quantum Monte Carlo (QMC) simulations combined with the many-particle localization length familiar from the modern theory of the insulating state. In the noninteracting limit, the critical optical-lattice intensity for the metal-insulator transition predicted by the QMC simulations coincides with the Anderson localization transition of the single-particle eigenstates. We show that weak repulsive interactions induce a shift of this critical point towards larger intensities, meaning that repulsion favors metallic behavior. This shift appears to be linear in the interaction parameter, suggesting that even infinitesimal interactions can affect the position of the critical point.
We use ultracold atoms in a quasiperiodic lattice to study two outstanding problems in the physics of disordered systems: a) the anomalous diffusion of a wavepacket in the presence of disorder, interactions and noise; b) the transport of a disordered superfluid.a) Our results show that the subdiffusion, observed when interaction alone is present, can be modelled with a nonlinear diffusion equation and the peculiar shape of the expanding density profiles can be connected to the microscopic nonlinear diffusion coefficients.Also when noise alone is present we can describe the observed normal diffusion dynamics by existing microscopic models.In the unexplored regime in which noise and interaction are combined, instead, we observe an anomalous diffusion, that we model with a generalized diffusion equation, where noise-and interaction-induced contributions add each other.b) We find that an instability appearing at relatively large momenta can be employed to locate the fluid-insulator crossover driven by disorder.By investigating the momentum-dependent transport, we observe a sharp crossover from a weakly dissipative regime to a strongly unstable one at a disorder-dependent critical momentum.The set of critical disorder and interaction strengths for which such critical momentum vanishes, can be identified with the separation between a fluid regime and an insulating one and can be related to the predicted zero-temperature superfluid-Bose glass transition.
We uncover a disorder-driven instability in the diffusive Fermi liquid phase of a class of many-fermion systems, indicative of a metal-insulator transition of first-order type, which arises solely from the competition between quenched disorder and interparticle interactions. Our result is expected to be relevant for sufficiently strong disorder in
d=3 spatial dimensions. Specifically, we study a class of half-filled, Hubbard-like models for spinless fermions with (complex) random hopping and short-ranged interactions on bipartite lattices in $d\ensuremath{\geqslant}2$. In a given realization, the hopping disorder breaks time-reversal invariance but preserves the special ``nesting'' symmetry responsible for the charge density wave instability of the ballistic Fermi liquid. This disorder may arise, e.g., from the application of a random magnetic field to the otherwise clean model. We derive a low-energy effective field theory description for this class of disordered, interacting fermion systems, which takes the form of a Finkel'stein nonlinear sigma model $(\mathrm{FNL}\ensuremath{\sigma}\mathrm{M})$ (A. M. Finkel'stein, Zh. Eksp. Teor. Fiz. 84, 168 (1983) [Sov. Phys. JETP 57, 97 (1983)]). We analyze the $\mathrm{FNL}\ensuremath{\sigma}\mathrm{M}$ using a perturbative, one-loop renormalization group analysis controlled via an
ϵ expansion in
d=2+ϵ dimensions. We find that in
d=2 dimensions, the interactions destabilize the conducting phase known to exist in the disordered, noninteracting system. The metal-insulator transition that we identify in
d>2 dimensions
(ϵ>0) occurs for disorder strengths of order
ϵ, and is therefore perturbatively accessible for
ϵ⪡1. We emphasize that the disordered system has no localized phase in the absence of interactions, so that a localized phase and the transition into it can only appear due to the presence of the interactions.