The crossover between two customary limits of phonon-assisted tunneling, the adiabatic and antiadiabatic regimes, is studied systematically in the framework of a minimal model for molecular devices: a resonant level coupled by displacement to a localized vibrational mode. Conventionally associated with the limits where the phonon frequency is either sufficiently small or sufficiently large as compared to the bare electronic hopping rate, we show that the crossover between the two regimes is governed for strong electron-phonon interactions primarily by the polaronic shift rather than the phonon frequency. In particular, the perturbative adiabatic limit is approached only as the bare hopping rate Γ exceeds the polaronic shift, leaving an extended window of couplings where Γ well exceeds the phonon frequency and yet the physics is basically that of the antiadiabatic regime. We term this intermediate regime the extended antiadiabatic regime. The effective lowenergy Hamiltonian in the traditional and the extended antiadiabatic regime is shown to be the (purely fermionic) interacting resonant-level model, with parameters that we extract from numerical renormalization-group calculations. The extended antiadiabatic regime is followed in turn by a true crossover region where the polaron gets progressively undressed. In this latter region, the phonon configuration strongly deviates from a simple superposition of just one or two coherent states. The renormalized tunneling rate, which serves as the low-energy scale in the problem and thus sets the width of the tunneling resonance, is found to follow an approximate scaling form on going from the adiabatic to the antiadiabatic regime. Charging properties are governed by two distinct mechanisms at the extended antiadiabatic and into the crossover region, giving rise to characteristic shoulders in the low-temperature conductance as a function of gate voltage. These shoulders serve as a distinct experimental fingerprint of phonon-assisted tunneling when the electron-phonon coupling is strong.

The time-dependent numerical renormalization-group approach (TD-NRG), originally devised for tracking the real-time dynamics of quantum-impurity systems following a single quantum quench, is extended to multiple switching events. This generalization of the TD-NRG encompasses the possibility of periodic switching, allowing for coherent control of strongly correlated systems by an external time-dependent field. To this end, we have embedded the TD-NRG in a hybrid framework that combines the outstanding capabilities of the numerical renormalization group to systematically construct the effective low-energy Hamiltonian of the system with the prowess of complementary approaches for calculating the real-time dynamics derived from this Hamiltonian. We demonstrate the power of our approach by hybridizing the TD-NRG with the Chebyshev expansion technique in order to investigate periodic switching in the interacting resonant-level model. Although the interacting model shares the same low-energy fixed point as its noninteracting counterpart, we surprisingly find the gradual emergence of damped oscillations as the interaction strength is increased. Focusing on a single quantum quench and using a strong-coupling analysis, we reveal the origin of these interaction-induced oscillations and provide an analytical estimate for their frequency. The latter agrees well with the numerical results.

A hybrid approach to nonequilibrium dynamics of quantum impurity systems is presented. The numerical renormalization group serves as a means to generate a suitable low-energy Hamiltonian, allowing for an accurate evaluation of the real-time dynamics of the problem up to exponentially long times using primarily the time-adaptive density-matrix renormalization group. We extract the decay time of the interaction-enhanced oscillations in the interacting resonant-level model and show their quadratic divergence with the interaction strength U . Our numerical analysis is in excellent agreement with analytic predictions based on an expansion in 1/U . Introduction. The description of strong electronic correlations far from thermal equilibrium poses an enormous theoretical challenge. At the root of the problem lies the nonequilibrium density operator which is not explicitly known in the presence of interactions. Of particular relevance are quench and driven dynamics realized in pump-probe experiments [1, 2], atomic traps [3,4], and nanodevices [5,6], where the full time evolution of the density operator should, in principle, be tracked.Quantum impurities systems (QIS) have regained considerable attention over the past 15 years due to the advent of carefully designed nanodevices. These generically consist of a few locally interacting degrees of freedom, typically a quantum dot, in contact with macroscopic leads. Since driven dynamics in nanodevices is of practical relevance to quantum computing and quantum control, considerable efforts were mounted in recent years toward devising approaches capable of treating the nonequilibrium state in QIS.Significant analytical progress in the calculation of real-time dynamics was achieved using different adaptations of perturbative renormalization-group ideas [7][8][9]. However, with the exception of Ref.[10], these are confined to the weak-coupling regime. Numerical methods, such as applications of the time-dependent densitymatrix renormalization group (TD-DMRG) [11,12] to QIS [13,14], the time-dependent numerical renormalization group (TD-NRG) [15], an iterated path-integral approach [16], and different continuous-time Monte Carlo simulations [17][18][19], are more flexible in the parameter regimes they can treat, but are either restricted to short time scales [13,14,[16][17][18][19] or susceptible to finite-size and discretization errors [13][14][15]. Indeed, finite-size representations are faced with an inherent difficulty of accurately representing the continuum limit even on intermediate time scales.In this paper, we report the extension of a recent hybrid approach [20] that overcomes some of the major ob-

We present a numerically exact Inchworm Monte Carlo method for equilibrium multiorbital quantum impurity problems with general interactions and hybridizations. We show that the method, originally developed to overcome the dynamical sign problem in certain real-time propagation problems, can also overcome the sign problem as a function of temperature for equilibrium quantum impurity models. This is shown in several cases where the current method of choice, the continuoustime hybridization expansion, fails due to the sign problem. Our method therefore enables simulations of impurity problems as they appear in embedding theories without further approximations, such as the truncation of the hybridization or interaction structure or a discretization of the impurity bath with a set of discrete energy levels, and eliminates a crucial bottleneck in the simulation of ab initio embedding problems.

We use the two-step density-matrix renormalization group method to elucidate the long-standing issue of the universality class of the Mott transition in the Hubbard model in two dimensions. We studied a spatially anisotropic two-dimensional Hubbard model with a non-perfectly nested Fermi surface at half-filling. We find that unlike the pure one-dimensional case where there is no metallic phase, the quasi one-dimensional model displays a genuine metal-insulator transition at a finite value of the interaction. The critical exponent of the correlation length is found to be ν ≈ 1.0. This implies that the fermionic Mott transition, belongs to the universality class of the 2D Ising model. The Mott insulator is the 'ordered' phase whose order parameter is given by the density of singly occupied sites minus that of holes and doubly occupied sites.

We report the application of the density-matrix renormalization group method to a spatially anisotropic two-dimensional Hubbard model at half-filling. We find a deconfinement transition induced by the transverse hopping parameter ty from an insulator to a metal. Therefore, if ty is fixed in the metallic phase, increasing the interaction U leads to a metal-to-insulator transition at a finite critical U . This is in contrast to the weak-coupling Hartree-Fock theory which predicts a nesting induced antiferromagnetic insulator for any U > 0.The metal-insulator transition (MIT), also called the Mott transition [1], is certainly one of the most difficult challenge facing condensed matter theorists. Hubbard [2], in a pioneering work, introduced a simple one-band Hamiltonian which has only two parameters, t for the kinetic energy of the electrons and U for the local electronelectron interactions. This model is at half-filling the model of reference for the MIT. In D = 1, Lieb and Wu [3] obtained an exact solution by using the Bethe ansatz. The ground state is an insulator for any U/W > 0, where W is the band width. Thus, the MIT occurs at the critical value (U/W ) c = 0. In infinite dimensions, the dynamical mean-field theory (DMFT) [4,5] predicts a critical point at (U/W ) c ≈ 1.The discovery of layered materials, where the motion of electrons driving the low energy physics is mostly confined in the layers, has raised great interest into the twodimensional (2D) Hubbard model. The physics at large U/W > ∼ 1 is now understood, the charge excitations are gapped, the spin excitation are described by the Heisenberg Hamiltonian which has long-range order (LRO) at T = 0. But for U/W < ∼ 1, the physics is still unclear. Our current knowledge about the weak-coupling regime is mostly drawn from the Hartree-Fock approximation and from quantum Monte Carlo (QMC) simulations [6,7]. The QMC results agree qualitatively with the HartreeFock prediction that the ground state is a Slater insulator for any U/W > 0. However, in most recent studies such as in Ref. [7], even though considerable progress has been achieved in reaching larger systems, in the weak U regime where the eventual gap is small, reliable extrapolations of the QMC data remain difficult to achieve. It would thus be preferable to apply finite size scaling for data analysis instead of relying on extrapolations.More recently, extensions of the DMFT which include non-local fluctuations, the dynamical cluster approximation (DCA) [8] or the cellular DMFT [9,10], have been applied to the 2D Hubbard model. The focus in these studies have mostly been to discuss the nature of the MIT within the paramagnetic solution of the DMFT equations. A systematic comparison of the possible ordered or disordered ground states as function of the cluster sizes is still lacking. Therefore, the issue as to whether or not quantum fluctuations destroy the Hartree-Fock solution in the half-filled 2D Hubbard model in the small U regime remains open.In this letter, we show that insight into this problem...

The quantum phase transition from a spin-Peierls phase with a small Fermi surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is studied in the framework of a onedimensional Kondo-Heisenberg model that consists of an electron gas away from half filling, coupled to a spin-1/2 chain by Kondo interactions. The Kondo spins are further coupled to each other with isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing on three-eighths filling and using the density-matrix renormalization-group (DMRG) method, we show that the zero-temperature transition between the phases with small and large Fermi momenta appears continuous, and involves a new intermediate phase where the Fermi surface is not well defined. The intermediate phase is spin gapped and has Kondo-spin correlations that show incommensurate modulations. Our results appear incompatible with the local picture for the quantum phase transition in heavy fermion compounds, which predicts an abrupt change in the size of the Fermi momentum.

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