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Register a new userSystematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method
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Gaussian Quantum Monte Carlo (GQMC) is a stochastic phase space method for fermions with positive weights. In the example of the Hubbard model close to half filling it fails to reproduce all the symmetries of the ground state leading to systematic errors at low temperatures. In a previous work [Phys. Rev. B {bf 72}, 224518 (2005)] we proposed to restore the broken symmetries by projecting the density matrix obtained from the simulation onto the ground state symmetry sector. For ground state properties, the accuracy of this method depends on a {it large overlap} between the GQMC and exact density matrices. Thus, the method is not rigorously exact. We present the limits of the approach by a systematic study of the method for 2 and 3 leg Hubbard ladders for different fillings and on-site repulsion strengths. We show several indications that the systematic errors stem from non-vanishing boundary terms in the partial integration step in the derivation of the Fokker-Planck equation. Checking for spiking trajectories and slow decaying probability distributions provides an important test of the reliability of the results. Possible solutions to avoid boundary terms are discussed. Furthermore we compare results obtained from two different sampling methods: Reconfiguration of walkers and the Metropolis algorithm.
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A novel sign-free Monte Carlo method for the Hubbard model has recently been proposed by Corney and Drummond. High precision measurements on small clusters show that ground state correlation functions are not correctly reproduced. We argue that the origin of this mismatch lies in the fact that the low temperature density matrix does not have the symmetries of the Hamiltonian. Here we show that supplementing the algorithm with symmetry projection schemes provides reliable and accurate estimates of ground state properties.
We present a systematic and comprehensive study of finite-size effects in diffusion quantum Monte Carlo calculations of metals. Several previously introduced schemes for correcting finite-size errors are compared for accuracy and efficiency and practical improvements are introduced. In particular, we test a simple but efficient method of finite-size correction based on an accurate combination of twist averaging and density functional theory. Our diffusion quantum Monte Carlo results for lithium and aluminum, as examples of metallic systems, demonstrate excellent agreement between all of the approaches considered.
In this work, we have reviewed the Oslo method, which enables the simultaneous extraction of level density and gamma-ray transmission coefficient from a set of particle-gamma coincidence data. Possible errors and uncertainties have been investigated. Typical data sets from various mass regions as well as simulated data have been tested against the assumptions behind the data analysis.
Using publicly available code and data, we present a systematic study of projection biases in the weak lensing analysis of the first year of data from the Dark Energy Survey (DES) experiment. In the analysis we used a $Lambda$CDM model and three two-point correlation functions. We show that these biases are a consequence of projecting, or marginalizing, over parameters like $h_0$, $Omega_b$, $n_s$ and $Omega_ u$ that are both poorly constrained and correlated with the parameters of interest like $Omega_m$, $sigma_8$ and $S_8$. Covering the relevant parameter space we show that the projection biases are a function of where the true values of the poorly constrained parameters lie with respect to the parameter priors. For example, biases can exceed the 1.5$sigma$ level if the true values of $h$ and $n_s$ are close to the top of the priors range and the true values of $Omega_b$ and $Omega_ u$ are close to the bottom of the range of their priors. We also show that in some cases the 1D confidence intervals can be over-specified by as much as 30%. Finally we estimate these projection biases for the analysis of three and six years worth of DES data.
We consider the effect of the coupling between 2D quantum rotors near an XY ferromagnetic quantum critical point and spins of itinerant fermions. We analyze how this coupling affects the dynamics of rotors and the self-energy of fermions.A common belief is that near a $mathbf{q}=0$ ferromagnetic transition, fermions induce an $Omega/q$ Landau damping of rotors (i.e., the dynamical critical exponent is $z=3$) and Landau overdamped rotors give rise to non-Fermi liquid fermionic self-energy $Sigmapropto omega^{2/3}$. This behavior has been confirmed in previous quantum Monte Carlo studies. Here we show that for the XY case the behavior is different. We report the results of large scale quantum Monte Carlo simulations, which clearly show that at small frequencies $z=2$ and $Sigmapropto omega^{1/2}$. We argue that the new behavior is associated with the fact that a fermionic spin is by itself not a conserved quantity due to spin-spin coupling to rotors, and a combination of self-energy and vertex corrections replaces $1/q$ in the Landau damping by a constant. We discuss the implication of these results to experiment
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