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The multiorbital Hubbard model is expressed in terms of quantum phase variables ("slave rotors") conjugate to the local charge, and of auxiliary fermions, providing an economical representation of the Hilbert space of strongly correlated systems. When the phase variables are treated in a local mean-field manner, similar results to the dynamical mean-field theory are obtained, namely a Brinkman-Rice transition at commensurate fillings together with a "preformed" Mott gap in the single-particle density of states. The slave-rotor formalism allows to go beyond the local description and take into account spatial correlations, following an analogy to the superfluid-insulator transition of bosonic systems. We find that the divergence of the effective mass at the metal-insulator transition is suppressed by short range magnetic correlations in finite-dimensional systems. Furthermore, the strict separation of energy scales between the Fermi-liquid coherence scale and the Mott gap, found in the local picture, holds only approximately in finite dimensions, due to the existence of low-energy collective modes related to zero-sound.

Quantum criticality is the intriguing possibility offered by the laws of quantum mechanics when the wave function of a many-particle physical system is forced to evolve continuously between two distinct, competing ground states. This phenomenon, often related to a zero-temperature magnetic phase transition, can be observed in several strongly correlated materials such as heavy fermion compounds or possibly high-temperature superconductors, and is believed to govern many of their fascinating, yet still unexplained properties. In contrast to these bulk materials with very complex electronic structure, artificial nanoscale devices could offer a new and simpler vista to the comprehension of quantum phase transitions. This long-sought possibility is demonstrated by our work in a fullerene molecular junction, where gate voltage induces a crossing of singlet and triplet spin states at zero magnetic field. Electronic tunneling from metallic contacts into the C60 quantum dot provides here the necessary many-body correlations to observe a true quantum critical behavior.

We have performed in-plane transport measurements on the two-dimensional organic salt κ-(BEDT-TTF)2Cu[N(CN)2]Cl. A variable (gas) pressure technique allows for a detailed study of the changes in conductivity through the insulator-to-metal transition. We identify four different transport regimes as a function of pressure and temperature (corresponding to insulating, semiconducting, "bad metal", and strongly correlated Fermi liquid behaviours). Marked hysteresis is found in the transition region, which displays complex physics that we attribute to strong spatial inhomogeneities. Away from the critical region, good agreement is found with a dynamical mean-field calculation of transport properties using the numerical renormalization group technique.

We introduce a representation of electron operators as a product of a spin-carry ing fermion and of a phase variable dual to the total charge (slave quantum rotor). Based on this representation, a new method is proposed for solving multi-orbital Anderson quantum impurity models at finite interaction strength U. It consists in a set of coupled integral equations for the auxiliary field Green's functions, which can be derived from a controlled saddle-point in the limit of a large number of field components. In contrast to some finite-U extensions of the non-crossing approximation, the new method provides a smooth interpolation between the atomic limit and the weak-coupling limit, and does not display violation of causality at low-frequency. We demonstrate that this impurity solver can be applied in the context of Dynamical Mean-Field Theory, at or close to half-filling. Good agreement with established results on the Mott transition is found, and large values of the orbital degeneracy can be investigated at low computational cost.Comment: 18 pages, 15 figure

We develop a general perturbative framework based on a superconducting atomic limit for the description of Andreev bound states ͑ABS͒ in interacting quantum dots connected to superconducting leads. A local effective Hamiltonian for dressed ABS, including both the atomic ͑or molecular͒ levels and the induced proximity effect on the dot is argued to be a natural starting point. A self-consistent expansion in single-particle tunneling events is shown to provide accurate results even in regimes where the superconducting gap is smaller than the atomic energies, as demonstrated by a comparison to recent numerical renormalization group calculations. This simple formulation may have bearings for interpreting Andreev spectroscopic experiments in superconducting devices, such as scanning tunnel microscope measurements on carbon nanotubes or radiative emission in optical quantum dots.

We present first quantitative experimental evidence for the underscreened Kondo effect, an uncomplete compensation of a quantized magnetic moment by conduction electrons, as originally proposed by Nozières and Blandin. The device consists of an even charge spin S = 1 molecular quantum dot, obtained by electromigration of C60 molecules into gold nanogaps and operated in a dilution fridge. The persistence of logarithmic singularities in the low temperature conductance is demonstrated by a comparison to the fully screened configuration obtained in odd charge spin S = 1/2 Coulomb diamonds. We also discover an extreme sensitivity of the underscreened Kondo resonance to magnetic field, that we confirm on the basis of numerical renormalization group calculations. PACS numbers:When a magnetic impurity is inserted in a piece of metal, its magnetic moment can be completely screened by the conduction electrons, owing to their quantized spin 1/2. This general phenomenon, the Kondo effect, has been thoroughly studied in diluted magnetic alloys [1] and has attracted considerable attention in the more recent quantum dot systems [2]. Clearly, impurities carrying a spin S greater that 1/2 need to bind several electronic orbitals in order to fully quench their magnetism, and Nature seems to conspire in always providing enough screening channels for that situation to occur in general [3]. Therefore, the possibility that screening may happen to be incomplete, as initially proposed on theoretical grounds by Nozières and Blandin [4], has remained elusive for almost thirty years, despite the great experimental control that one can achieve with artificial quantum dot setups. The observation of the underscreened Kondo effect, in addition to its overscreened counterpart [5], is also especially appealing since it constitutes one of the simplest cases where standard Fermi Liquid Theory is violated [6,7].We demonstrate in this Letter that molecular quantum dots obtained through electromigration [8] are perfect candidates for achieving underscreened Kondo impurities. Indeed point contact tunneling (single mode) and important left/right asymmetry of the transport electrodes ensure a large window of energies where a single screening channel is active. In addition, the Kondo phenomenon in molecules can set in already at several kelvins [9,10,11,12] thanks to relatively important charging energies, allowing a complete study of Kondo crossovers on a sufficient range of temperatures. Both conditions of single channel and large Kondo temperature are difficult to meet altogether in other quantum dot devices, where Kondo effects associated with higher spin states have been previously found, but yet not investigated in detail [13,14,15,16,17]. We report here on the first observation of the anomalous logarithmic behavior in the temperature and bias voltage dependent conductance in a spin S = 1 quantum dot below the Kondo scale, as previously predicted for underscreened impurities [4,6,7,18], and successfully confront our results with quantitative nume...

The key feature of a quantum spin coupled to a harmonic bath-a model dissipative quantum system-is competition between oscillator potential energy and spin tunneling rate. We show that these opposing tendencies cause environmental entanglement through superpositions of adiabatic and antiadiabatic oscillator states, which then stabilizes the spin coherence against strong dissipation. This insight motivates a fast-converging variational coherent-state expansion for the many-body ground state of the spin-boson model, which we substantiate via numerical quantum tomography.arXiv:1307.5681v2 [quant-ph]

We develop a systematic variational coherent state expansion for the many-body ground state of the spin-boson model, in which a quantum two-level system is coupled to a continuum of harmonic oscillators. Energetic constraints at the heart of this technique are rationalized in terms of polarons (displacements of the bath states in agreement with classical expectations) and antipolarons (counterdisplacements due to quantum tunneling effects). We present a comprehensive study of the ground state two-level system population and coherence as a function of tunneling amplitude, dissipation strength, and bias (akin to asymmetry of the double well potential defining the two-state system). The entanglement among the different environmental modes is investigated by looking at spectroscopic signatures of the bipartite entanglement entropy between a given environmental mode and all the other modes. We observe a drastic change in behavior of this entropy for increasing dissipation, indicative of the entangled nature of the environmental states. In addition, the entropy spreads over a large energy range at strong dissipation, a testimony to the wide entanglement window characterizing the underlying Kondo state. Finally, comparisons to accurate numerical renormalization group calculations and to the exact Bethe Ansatz solution of the model demonstrate the rapid convergence of our variationally-optimized multi-polaron expansion, suggesting that it should also be a useful tool for dissipative models of greater complexity, as relevant for numerous systems of interest in quantum physics and chemistry.

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