Toward Large-Scale Restricted Active Space Calculations Inspired by the Schmidt Decomposition.

We present an alternative, memory-efficient, Schmidt decomposition-based description of the inherently bipartite restricted active space (RAS) scheme, which can be implemented effortlessly within the density matrix renormalization group (DMRG) method via the dynamically extended active space procedure. Benchmark calculations are compared against state-of-the-art results of C2 and Cr2, which are notorious for their multireference character. Our results for ground and excited states together with spectroscopic constants demonstrate that the proposed novel approach, dubbed as DMRG-RAS, which is variational and free of uncontrolled method errors, has the potential to outperfom conventional methods for strongly correlated molecules.

Kondo Cloud in a Superconductor.

Magnetic impurities embedded in a metal are screened by the Kondo effect, signaled by the formation of an extended correlation cloud, the so-called Kondo or screening cloud. In a superconductor, the Kondo state turns into subgap Yu-Shiba-Rusinov states, and a quantum phase transition occurs between screened and unscreened phases once the superconducting energy gap Δ exceeds sufficiently the Kondo temperature, T_{K}. Here we show that, although the Kondo state does not form in the unscreened phase, the Kondo cloud does exist in both quantum phases. However, while screening is complete in the screened phase, it is only partial in the unscreened phase. Compensation, a quantity introduced to characterize the integrity of the cloud, is universal, and shown to be related to the magnetic impurities' g factor, monitored experimentally by bias spectroscopy.

Universal Scaling Theory of the Boundary Geometric Tensor in Disordered Metals.

We investigate the finite-size scaling of the boundary quantum geometric tensor (QGT) numerically close to the Anderson localization transition in the presence of small external magnetic fields. The QGT exhibits universal scaling and reveals the crossover between the orthogonal and unitary critical states in weak random magnetic fields. The flow of the QGT near the critical points determines the critical exponents. Critical distributions of the QGT are universal and exhibit a remarkable isotropy even in a homogeneous magnetic field. We predict universal and isotropic Hall conductance fluctuations at the metal-insulator transition in an external magnetic field.

Selective state spectroscopy and multifractality in disordered Bose-Einstein condensates: a numerical study.

We propose to apply a modified version of the excitation scheme introduced by Volchkov et al. on bosons experiencing hyperfine state dependent disorder to address the critical state at the mobility edge of the Anderson localization transition, and to observe its intriguing multifractal structure. An optimally designed, spatially focused external radio frequency pulse can be applied to generate transitions to eigenstates in a narrow energy window close to the mobility edge, where critical scaling and multifractality emerge. Alternatively, two-photon laser scanning microscopy is proposed to address individual localized states even close to the transition. The projected image of the cloud is shown to inherit multifractality and to display universal density correlations. Interactions - unavoidably present - are taken into account by solving the Gross-Pitaevskii equations, and their destructive effect on the spectral resolution and the multifractal spectrum is analyzed. Time of flight images of the excited states are predicted to show interference fringes in the localized phase, while they allow one to map equal energy surfaces deep in the metallic phase.