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.

Classical theory of universal quantum work distribution in chaotic and disordered non-interacting Fermi systems.

We present a universal theory of quantum work statistics in generic disordered non-interacting Fermi systems, displaying a chaotic single-particle spectrum captured by random matrix theory. We consider quantum quenches both within a driven random matrix formalism and in an experimentally accessible microscopic model, describing a two-dimensional disordered quantum dot. By extending Anderson's orthogonality determinant formula to compute quantum work distribution, we demonstrate that work statistics is non-Gaussian and is characterized by a few dimensionless parameters. At longer times, quantum interference effects become irrelevant and the quantum work distribution is well-described in terms of a purely classical ladder model with a symmetric exclusion process in energy space, while bosonization and mean field methods provide accurate analytical expressions for the work statistics. Our results demonstrate the universality of work distribution in generic chaotic Fermi systems, captured by the analytical predictions of a mean field theory, and can be verified by calorimetric measurements on nanoscale circuits.

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.

Bilayer Wigner crystals in a transition metal dichalcogenide heterostructure.

One of the first theoretically predicted manifestations of strong interactions in many-electron systems was the Wigner crystal1-3, in which electrons crystallize into a regular lattice. The crystal can melt via either thermal or quantum fluctuations4. Quantum melting of the Wigner crystal is predicted to produce exotic intermediate phases5,6 and quantum magnetism7,8 because of the intricate interplay of Coulomb interactions and kinetic energy. However, studying two-dimensional Wigner crystals in the quantum regime has often required a strong magnetic field9-11 or a moiré superlattice potential12-15, thus limiting access to the full phase diagram of the interacting electron liquid. Here we report the observation of bilayer Wigner crystals without magnetic fields or moiré potentials in an atomically thin transition metal dichalcogenide heterostructure, which consists of two MoSe2 monolayers separated by hexagonal boron nitride. We observe optical signatures of robust correlated insulating states at symmetric (1:1) and asymmetric (3:1, 4:1 and 7:1) electron doping of the two MoSe2 layers at cryogenic temperatures. We attribute these features to bilayer Wigner crystals composed of two interlocked commensurate triangular electron lattices, stabilized by inter-layer interaction16. The Wigner crystal phases are remarkably stable, and undergo quantum and thermal melting transitions at electron densities of up to 6 × 1012 per square centimetre and at temperatures of up to about 40 kelvin. Our results demonstrate that an atomically thin heterostructure is a highly tunable platform for realizing many-body electronic states and probing their liquid-solid and magnetic quantum phase transitions4-8,17.

Hilbert Space Geometry of Random Matrix Eigenstates.

The geometry of multiparameter families of quantum states is important in numerous contexts, including adiabatic or nonadiabatic quantum dynamics, quantum quenches, and the characterization of quantum critical points. Here, we discuss the Hilbert space geometry of eigenstates of parameter-dependent random matrix ensembles, deriving the full probability distribution of the quantum geometric tensor for the Gaussian unitary ensemble. Our analytical results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We discuss relations to Levy stable distributions and compare our results to numerical simulations of random matrix ensembles as well as electrons in a random magnetic field.

Topologically Protected Correlated End Spin Formation in Carbon Nanotubes.

For most chiralities, semiconducting nanotubes display topologically protected end states of multiple degeneracies. We demonstrate using density matrix renormalization group based quantum chemistry tools that the presence of Coulomb interactions induces the formation of robust end spins. These are the close analogs of ferromagnetic edge states emerging in graphene nanoribbons. The interaction between the two ends is sensitive to the length of the nanotube, its dielectric constant, and the size of the end spins: for S=1/2 end spins, their interaction is antiferromagnetic, while for S>1/2, it changes from antiferromagnetic to ferromagnetic as the nanotube length increases. The interaction between end spins can be controlled by changing the dielectric constant of the environment, thereby providing a possible platform for two-spin quantum manipulations.

Large spatial extension of the zero-energy Yu-Shiba-Rusinov state in a magnetic field.

Various promising qubit concepts have been put forward recently based on engineered superconductor subgap states like Andreev bound states, Majorana zero modes or the Yu-Shiba-Rusinov (Shiba) states. The coupling of these subgap states via a superconductor strongly depends on their spatial extension and is an essential next step for future quantum technologies. Here we investigate the spatial extension of a Shiba state in a semiconductor quantum dot coupled to a superconductor. With detailed transport measurements and numerical renormalization group calculations we find a remarkable more than 50 nm extension of the zero energy Shiba state, much larger than the one observed in very recent scanning tunneling microscopy measurements. Moreover, we demonstrate that its spatial extension increases substantially in a magnetic field.

Vaporization Dynamics of a Dissipative Quantum Liquid.

We investigate the stability of a Luttinger liquid, upon suddenly coupling it to a dissipative environment. Within the Lindblad equation, the environment couples to local currents and heats the quantum liquid up to infinite temperatures. The single particle density matrix reveals the fractionalization of fermionic excitations in the spatial correlations by retaining the initial noninteger power law exponents, accompanied by an exponential decay in time with an interaction dependent rate. The spectrum of the time evolved density matrix is gapped, which collapses gradually as -ln(t). The von Neumann entropy crosses over from the early time -tln(t) behavior to ln(t) growth for late times. The early time dynamics is captured numerically by performing simulations on spinless interacting fermions, using several numerically exact methods. Our results could be tested experimentally in bosonic Luttinger liquids.

Quantum Criticality and Formation of a Singular Fermi Liquid in the Attractive SU(N>2) Anderson Model.

While much is known about repulsive quantum impurity models, significantly less attention has been devoted to their attractive counterparts. This motivated us to study the attractive SU(N) Anderson impurity model. While for the repulsive case the phase diagram features mild N dependence and the ground state is always a Fermi liquid, in the attractive case a Kosterlitz-Thouless charge localization phase transition is revealed for N>2. Beyond a critical value of attractive interaction, an abrupt jump appears in the number of particles at the impurity site, and a singular Fermi liquid state emerges, where the scattering of quasiparticles is found to exhibit power law behavior with fractional power. The capacity diverges exponentially at the quantum critical point, signaling the Kosterlitz-Thouless transition.

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.

Noise of a Chargeless Fermi Liquid.

We construct a Fermi liquid theory to describe transport in a superconductor-quantum dot-normal metal junction close to the singlet-doublet (parity changing) transition of the dot. Though quasiparticles do not have a definite charge in this chargeless Fermi liquid, in the case of particle-hole symmetry, a mapping to the Anderson model unveils a hidden U(1) symmetry and a corresponding pseudocharge. In contrast to other correlated Fermi liquids, the back scattering noise reveals an effective charge equal to the charge of Cooper pairs, e^{*}=2e. In addition, we find a strong suppression of noise when the linear conductance is unitary, even for its nonlinear part.

Hybrid Semiclassical Theory of Quantum Quenches in One-Dimensional Systems.

We develop a hybrid semiclassical method to study the time evolution of one-dimensional quantum systems in and out of equilibrium. Our method handles internal degrees of freedom completely quantum mechanically by a modified time-evolving block decimation method while treating orbital quasiparticle motion classically. We can follow dynamics up to time scales well beyond the reach of standard numerical methods to observe the crossover between preequilibrated and locally phase equilibrated states. As an application, we investigate the quench dynamics and phase fluctuations of a pair of tunnel-coupled one-dimensional Bose condensates. We demonstrate the emergence of soliton-collision-induced phase propagation, soliton-entropy production, and multistep thermalization. Our method can be applied to a wide range of gapped one-dimensional systems.

Loschmidt echo and the many-body orthogonality catastrophe in a qubit-coupled Luttinger liquid.

We investigate the many-body generalization of the orthogonality catastrophe by studying the generalized Loschmidt echo of Luttinger liquids (LLs) after a global change of interaction. It decays exponentially with system size and exhibits universal behavior: the steady state exponent after quenching back and forth n times between 2 LLs (bang-bang protocol) is 2n times bigger than that of the adiabatic overlap and depends only on the initial and final LL parameters. These are corroborated numerically by matrix-product state based methods of the XXZ Heisenberg model. An experimental setup consisting of a hybrid system containing cold atoms and a flux qubit coupled to a Feshbach resonance is proposed to measure the Loschmidt echo using rf spectroscopy or Ramsey interferometry.

An electrically controlled quantum dot based spin current injector.

We present a proposal for a fully electrically controllable quantum dot based spin current injector. The device consists of a quantum dot that is strongly coupled to a ferromagnetic electrode on one side and weakly coupled to a nonmagnetic electrode on the other side. The presence of the ferromagnetic electrode results in an exchange field that splits the dot level. We show that this exchange-induced splitting can lead to almost full spin polarization of the current flowing through the device. Moreover, we also demonstrate that the sign of polarization can be changed by the gate or the bias voltage within a switching time in the nanosecond range. Thus, the proposed device can operate as an electrically controlled, rapidly switchable spin current source, which can be realized in various state-of-the-art nanostructures.

Crossover from adiabatic to sudden interaction quench in a Luttinger liquid.

Motivated by recent experiments on interacting cold atoms, we analyze interaction quenches in Luttinger liquids (LLs), where the interaction is ramped from zero to a finite value within a finite time. The fermionic single particle density matrix reveals several regions of spatial and temporal coordinates relative to the quench time, termed as Fermi liquid, sudden quench LL, adiabatic LL regime, and a LL regime with a time-dependent exponent. The various regimes can also be observed in the momentum distribution of the fermions, directly accessible through time of flight experiments. Most of our results apply to arbitrary quench protocols.

Disordered one-dimensional bose-fermi mixtures: the Bose-Fermi glass.

We analyze an interacting Bose-Fermi mixture in a 1D disordered potential by using a combination of renormalization group and variational methods. We obtain the complete phase diagram in the incommensurate case as a function of bosonic and interspecies interaction strengths, in the weak disorder limit. We find that the system is characterized by several phase transitions between superfluid and various glassy insulating states, including a new Bose-Fermi glass phase, where both species are coupled and localized. We show that the dynamical structure factor, as measured through Bragg scattering experiments, can distinguish between the various localized phases and probe their dynamics.

Anomalous Hall effect in a two dimensional electron gas with magnetic impurities.

Magnetic impurities play an important role in many spintronics-related materials. Motivated by this fact, we study the anomalous Hall effect in the presence of magnetic impurities, focusing on two-dimensional electron systems with Rashba spin-orbit coupling. We find a highly nonlinear dependence on the impurity polarization, including possible sign changes. At small impurity magnetizations, this is a consequence of the remarkable result that the linear term is independent of the spin-orbit coupling strength. Near saturation of the impurity spins, the anomalous Hall conductivity can be resonantly enhanced, due to interference between potential and magnetic scattering.

Color superfluidity and "baryon" formation in ultracold fermions.

We study fermionic atoms of three different internal quantum states (colors) in an optical lattice, which are interacting through attractive on site interactions, U<0. Using a variational calculation for equal color densities and small couplings, |U|<|UC|, a color superfluid state emerges with a tendency to domain formation. For |U|>|UC|, triplets of atoms with different colors form singlet fermions (trions). These phases are the analogies of the color superconducting and baryonic phases in QCD. In ultracold fermions, this transition is found to be of second order. Our results demonstrate that quantum simulations with ultracold gases may shed light on outstanding problems in quantum field theory.

Quantum criticality in a double-quantum-dot system.

We discuss the realization of the quantum-critical non-Fermi-liquid state, originally discovered within the two-impurity Kondo model, in double-quantum-dot systems. Contrary to common belief, the corresponding fixed point is robust against particle-hole and various other asymmetries and is unstable only to charge transfer between the two dots. We propose an experimental setup where such charge transfer processes are suppressed, allowing a controlled approach to the quantum-critical state. We also discuss transport and scaling properties in the vicinity of the critical point.