Dynamical mean-field theory allows access to the physics of strongly correlated materials with nontrivial orbital structure, but relies on the ability to solve auxiliary multi-orbital impurity problems. The most successful approaches to date for solving these impurity problems are the various continuous time quantum Monte Carlo algorithms. Here, we consider perhaps the simplest realization of multi-orbital physics: the bilayer Hubbard model on an infinite-coordination Bethe lattice. Despite its simplicity, the majority of this model's phase diagram cannot be predicted by using traditional Monte Carlo methods. We show that these limitations can be largely circumvented by recently introduced Inchworm Monte Carlo techniques. We then explore the model's phase diagram at a variety of interaction strengths, temperatures and filling ratios.

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 continuous-time 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.

The rapid development of better high pressure experimental techniques combined with efficient and accurate density functional calculations of the structural properties of materials provide a new avenue to promote the study of materials at high pressures, which is currently based mostly on simple phenomenological modelling. The progress of experimental results into higher-pressure regimes represents a challenge to the phenomenological approaches, which can be addressed by carefully considered ab initio calculations. We present cold curves of several elements, calculated using different approximations of DFT and compare them with available experimental data. The comparison shows good agreement both in simple single phase and complex multi-phase cases. It suggests that DFT may be used to extrapolate high pressure behaviour of materials beyond the currently possible pressure range, with a robust estimate of the accuracy of the extrapolation based on various DFT implementations.

Is it possible for the organizers of a sports tournament to influence the identity of the final winner by manipulating the initial seeding of the tournament? Is it possible to ensure a specific good (i.e. king) player will win at least a certain number of rounds in the tournament? This paper investigates these questions both by means of a theoretical method and a practical approach. The theoretical method focuses on the attempt to identify sufficient conditions to ensure a king player will win at least a pre–defined number of rounds in the tournament. It seems that the tournament must adhere to very strict conditions to ensure the outcome, suggesting that this is a hard problem. The practical approach, on the other hand, uses the Monte Carlo method to demonstrate that these problems are solvable in realistic computational time. A comparison of the results lead to the realization that players with equivalent representation might relax the actual complexity of the problem, and enable manipulation of tournaments that can be controlled in reality.

Negative thermal expansion is an uncommon phenomenon of theoretical interest. Multiple hypotheses regarding its microscopic origins have been suggested. In this paper, the thermal expansion of a representative semiconductor, Si, and a representative metal, Ti, are calculated ab initio using density-functional perturbation theory. The phonon modes' contributions to the thermal expansion are analyzed and the negative thermal expansion is shown to be dominated by negative mode Gr\"uneisen parameters at specific points on the Brillouin zone boundaries. Thus, the elastic (Debye) theory for negative thermal expansion is shown to be irrelevant for these phenomena. The anomalous behavior of these modes in Ti is shown to be unaffected by an electronic topological transition as previously suggested, instead it arises from complex interplay of atomic displacements of the anomalous mode.

— Sound velocity measurements are an important tool for investigating phase transitions and calibrating the EOS outside the princi-ple Hugoniot. Two common methods are the overtake method and reverse-impact method. Although widely used, there is little discussion about the uncertainties of these methods. A comparison between the aforementioned methods for determining the sound velocity of shock compressed Al1100 is presented. The experiment con-sisted of an Al1100 flyer plate which was accelerated to velocity of 2.2 km/s towards two Al1100 targets of different thickness backed by a PMMA window and a third LiF target. This experiment was complimented by a second reverse-impact experiment in which an Al1100 flyer plate impacted a LiF target. The similarities of the shock impedance of LiF and Al1100 were used in order to achieve the same pressure in both of the experimental methods. The design of these experiments was led by detailed calculations in order to achieve minimal uncertainties in each experiment. These calculations took into account 2D effects such as edge rarefactions originating in the flyer plate, targets and windows. The uncertainty in the sound velocity is compared to our uncertainty estimate which was based on calculations.

The lattice parameters, lattice stability and phonon dispersion curves of five proposed phases of Ti: alpha, beta, gamma, delta and omega are investigated within DFT. It is found that the sequence of high pressure phases at zero temperature is alpha, omega, gamma, delta and beta with the delta and beta phases becoming degenerate at high pressure. However, the gamma phase may be unstable as is reflected by the existence of imaginary values in the phonon spectra. The results of the DFT calculations are employed to estimate the entropy and free energies of the alpha and omega phases. It is found that converged phonon calculations lead to an entropy difference which is much smaller than previous estimates, and a much steeper alpha-omega phase transition line.

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 \Gamma exceeds the polaronic shift, leaving an extended window of couplings where \Gamma 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 low-energy 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. 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 distinctive shoulders in the low-temperature conductance as a function of gate voltage.

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.

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.

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 nonperfectly 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 $\ensuremath{\nu}\ensuremath{\approx}1.0$. This implies that the fermionic Mott transition belongs to the universality class of the 2D Ising model.

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 t(y) from an insulator to a metal. Therefore, if t(y) 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 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 one-dimensional 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.

We report a two-step density-matrix renormalization-group computation of the equal-time single-particle Green's function, the density-density correlations, and the low-frequency spectral weight function of a spinless fermion model in an anisotropic two-dimensional lattice at half filling. We find that at weak couplings the density-density correlations have the universal decay of a Fermi liquid; the spectral weight function displays a sharp quasiparticle peak. But in the vicinity of a quantum critical point, these correlations strongly deviate from a Fermi-liquid prediction and a pseudogap opens in the spectral weight function.