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We present exact numerical data for the lowest-energy momentum eigenstates (yrast states) of a repulsive spin impurity in a one-dimensional Bose gas using full configuration interaction quantum Monte Carlo (FCIQMC). As a stochastic extension to exact diagonalization it is well suited for the study of yrast states of a lattice-renormalized model for a quantum gas. Yrast states carry valuable information about the dynamic properties of slow-moving mobile impurities immersed in a many-body system. Based on the energies and the first and second order correlation functions of yrast states, we identify different dynamical regimes and the transitions between them: The polaron regime, where the impurity's motion is affected by the Bose gas through a renormalized effective mass; a regime of a gray soliton that is weakly correlated with a stationary impurity, and the depleton regime, where the impurity occupies a dark or gray soliton. Extracting the depleton effective mass reveals a super heavy regime where the magnitude of the (negative) depleton mass exceeds the mass of the finite Bose gas., Comment: 22 pages, 8 figures; revised after peer-reviews

We investigate a systematic statistical bias found in full configuration quantum Monte Carlo (FCIQMC) that originates from controlling a walker population with a fluctuating shift parameter. This bias can become the dominant error when the sign problem is absent, e.g. in bosonic systems. FCIQMC is a powerful statistical method for obtaining information about the ground state of a sparse and abstract matrix. We show that, when the sign problem is absent, the shift estimator has the nice property of providing an upper bound for the exact ground state energy and all projected energy estimators, while a variational estimator is still an upper bound to the exact energy with substantially reduced bias. A scalar model of the general FCIQMC population dynamics leads to an exactly solvable It\^o stochastic differential equation. It provides further insights into the nature of the bias and gives accurate analytical predictions for delayed cross-covariance and auto-covariance functions of the shift energy estimator and the walker number. The model provides a toe-hold on finding a cure for the population control bias. We provide evidence for non-universal power-law scaling of the population control bias with walker number in the Bose-Hubbard model for various estimators of the ground state energy based on the shift or on projected energies. For the specific case of the non-interacting Bose-Hubbard Hamiltonian we obtain a full analytical prediction for the bias of the shift energy estimator., Comment: 24 pages, 14 figures; fixed typo in Eq. (72)

Full configuration interaction quantum Monte Carlo (FCIQMC) is a stochastic approach for finding the ground state of a quantum many-body Hamiltonian. It is based on the dynamical evolution of a walker population in Hilbert space, which samples the ground state configuration vector over many iterations. Here we present a modification of the original protocol for walker population control of Booth et al. JCP 131, 054106 (2009) in order to achieve equilibration at a pre-defined average walker number and to avoid walker number overshoots. The dynamics of the walker population is described by a noisy damped harmonic oscillator and controlled by two parameters responsible for damping and forcing, respectively, for which reasonable values are suggested. We further introduce a population growth witness that can be used to detect annihilation plateaus related to overcoming the FCIQMC sign problem. Features of the new population control procedure such as precise walker number control and fast equilibration are demonstrated. The standard error of the shift estimator for the ground state energy as well as the population control bias are found to be unaffected by the population control procedure or its parameters. The improved control of the walker number, and thereby memory consumption, is a desirable feature required for automating FCIQMC calculations and requires minimal modifications to existing code., Comment: 15 pages, 10 figures. Submitted to the Journal of Chemical Physics

The frozen local hole approximation (FLHA) is an adiabatic approximation which is aimed to simplify the correlation calculations of valence and conduction bands of solids and polymers. Within this approximation correlated local hole states (CLHSs) are explicitely generated by correlating local Hartree-Fock (HF) hole states. The hole orbital and its occupancy is kept frozen during these correlation calculations. Effective Hamilton matrix elements are then evaluated with the above CLHSs; diagonalization finally yields the desired correlation corrections for the cationic hole states. We compare and analyze the results of the FLHA with the results of a full MRCI(SD) (multi-reference configuration interaction with single and double excitations) calculation for two prototype model systems, (H2)n ladders and H-(Be)n-H chains. Excellent numerical agreement between the two approaches is found. Comparing the FLHA with a full correlation treatment in the framework of quasi-degenerate variational perturbation theory reveals that the leading contributions in the two approaches are identical. Thus, the FLHA is well-justified and provides a very promising and efficient alternative to fully correlated wavefunction-based treatments of the valence and conduction bands in extended systems., Comment: RevTeX, 9 pages, 7 figures (6 ps files)