Loop algorithms for quantum simulations of fermion models on lattices

Two cluster algorithms, based on constructing and flipping loops, are presented for worldline quantum Monte Carlo simulations of fermions and are tested on the one-dimensional repulsive Hubbard model. We call these algorithms the loop-flip and loop-exchange algorithms. For these two algorithms and the standard worldline algorithm, we calculated the autocorrelation times for various physical quantities and found that the ordinary worldline algorithm, which uses only local moves, suffers from very long correlation times that makes not only the estimate of the error difficult but also the estimate of the average values themselves difficult. These difficulties are especially severe in the low-temperature, large-$U$ regime. In contrast, we find that new algorithms, when used alone or in combinations with themselves and the standard algorithm, can have significantly smaller autocorrelation times, in some cases being smaller by three orders of magnitude. The new algorithms, which use non-local moves, are discussed from the point of view of a general prescription for developing cluster algorithms. The loop-flip algorithm is also shown to be ergodic and to belong to the grand canonical ensemble. Extensions to other models and higher dimensions is briefly discussed.Comment: 36 pages, RevTex ver.

Multiple Histogram Method for Quantum Monte Carlo

An extension to the multiple-histogram method (sometimes referred to as the Ferrenberg-Swendsen method) for use in quantum Monte Carlo simulations is presented. This method is shown to work well for the 2D repulsive Hubbard model, allowing measurements to be taken over a continuous region of parameters. The method also reduces the error bars over the range of parameter values due the overlapping of multiple histograms. A continuous sweep of parameters and reduced error bars allow one to make more difficult measurements, such as Maxwell constructions used to study phase separation. Possibilities also exist for this method to be used for other quantum systems.Comment: 4 pages, 5 figures, RevTeX, submitted to Phys. Rev. B Rapid Com

A Constrained Path Quantum Monte Carlo Method for Fermion Ground States

We propose a new quantum Monte Carlo algorithm to compute fermion ground-state properties. The ground state is projected from an initial wavefunction by a branching random walk in an over-complete basis space of Slater determinants. By constraining the determinants according to a trial wavefunction $|\Psi_T \rangle$, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if $|\Psi_T\rangle$ is exact. We report results on the two-dimensional Hubbard model up to size $16\times 16$, for various electron fillings and interaction strengths.Comment: uuencoded compressed postscript file. 5 pages with 1 figure. accepted by PRL

Localized Exotic Smoothness

Gompf's end-sum techniques are used to establish the existence of an infinity of non-diffeomorphic manifolds, all having the same trivial ${\bf R^4}$ topology, but for which the exotic differentiable structure is confined to a region which is spatially limited. Thus, the smoothness is standard outside of a region which is topologically (but not smoothly) ${\bf B^3}\times {\bf R^1}$, where ${\bf B^3}$ is the compact three ball. The exterior of this region is diffeomorphic to standard ${\bf R^1}\times {\bf S^2}\times{\bf R^1}$. In a space-time diagram, the confined exoticness sweeps out a world tube which, it is conjectured, might act as a source for certain non-standard solutions to the Einstein equations. It is shown that smooth Lorentz signature metrics can be globally continued from ones given on appropriately defined regions, including the exterior (standard) region. Similar constructs are provided for the topology, ${\bf S^2}\times {\bf R^2}$ of the Kruskal form of the Schwarzschild solution. This leads to conjectures on the existence of Einstein metrics which are externally identical to standard black hole ones, but none of which can be globally diffeomorphic to such standard objects. Certain aspects of the Cauchy problem are also discussed in terms of ${\bf R^4_\Theta}$\models which are ``half-standard'', say for all $t<0,$ but for which $t$ cannot be globally smooth.Comment: 8 pages plus 6 figures, available on request, IASSNS-HEP-94/2

Supersymmetric mass spectra and the seesaw type-I scale

We calculate supersymmetric mass spectra with cMSSM boundary conditions and a type-I seesaw mechanism added to explain current neutrino data. Using published, estimated errors on SUSY mass observables for a combined LHC+ILC analysis, we perform a theoretical $\chi^2$ analysis to identify parameter regions where pure cMSSM and cMSSM plus seesaw type-I might be distinguishable with LHC+ILC data. The most important observables are determined to be the (left) smuon and selectron masses and the splitting between them, respectively. Splitting in the (left) smuon and selectrons is tiny in most of cMSSM parameter space, but can be quite sizeable for large values of the seesaw scale, $m_{SS}$. Thus, for very roughly $m_{SS} \ge 10^{14}$ GeV hints for type-I seesaw might appear in SUSY mass measurements. Since our numerical results depend sensitively on forecasted error bars, we discuss in some detail the accuracies, which need to be achieved, before a realistic analysis searching for signs of type-I seesaw in SUSY spectra can be carried out.Comment: 17 pages, 7 figure

Charge and Spin Structures of a dx2−y2d_{x^2 - y^2} Superconductor in the Proximity of an Antiferromagnetic Mott Insulator

To the Hubbard model on a square lattice we add an interaction, $W$, which depends upon the square of a near-neighbor hopping. We use zero temperature quantum Monte Carlo simulations on lattice sizes up to $16 \times 16$, to show that at half-filling and constant value of the Hubbard repulsion, the interaction $W$ triggers a quantum transition between an antiferromagnetic Mott insulator and a $d_{x^2 -y^2}$ superconductor. With a combination of finite temperature quantum Monte Carlo simulations and the Maximum Entropy method, we study spin and charge degrees of freedom in the superconducting state. We give numerical evidence for the occurrence of a finite temperature Kosterlitz-Thouless transition to the $d_{x^2 -y^2}$ superconducting state. Above and below the Kosterlitz-Thouless transition temperature, $T_{KT}$, we compute the one-electron density of states, $N(\omega)$, the spin relaxation rate $1/T_1$, as well as the imaginary and real part of the spin susceptibility $\chi(\vec{q},\omega)$. The spin dynamics are characterized by the vanishing of $1/T_1$ and divergence of $Re \chi(\vec{q} = (\pi,\pi), \omega = 0)$ in the low temperature limit. As $T_{KT}$ is approached $N(\omega)$ develops a pseudo-gap feature and below $T_{KT}$ $Im \chi(\vec{q} = (\pi,\pi), \omega)$ shows a peak at finite frequency.Comment: 46 pages (latex) including 14 figures in encapsulated postscript format. Submitted for publication in Phys. Rev.

Finite-Temperature Monte Carlo Calculations For Systems With Fermions

We present a quantum Monte Carlo method which allows calculations on many-fermion systems at finite temperatures without any sign decay. This enables simulations of the grand-canonical ensemble at large system sizes and low temperatures. Both diagonal and off-diagonal expectations can be computed straightforwardly. The sign decay is eliminated by a constraint on the fermion determinant. The algorithm is approximate. Tests on the Hubbard model show that accurate results on the energy and correlation functions can be obtained.Comment: 5 pages, RevTex; to appear in Phys. Rev. Let

Random Exchange Quantum Heisenberg Chains

The one-dimensional quantum Heisenberg model with random $\pm J$ bonds is studied for $S=\frac{1}{2}$ and $S=1$. The specific heat and the zero-field susceptibility are calculated by using high-temperature series expansions and quantum transfer matrix method. The susceptibility shows a Curie-like temperature dependence at low temperatures as well as at high temperatures. The numerical results for the specific heat suggest that there are anomalously many low-lying excitations. The qualitative nature of these excitations is discussed based on the exact diagonalization of finite size systems.Comment: 13 pages, RevTex, 12 figures available on request ([email protected]

Dark matter scenarios in the minimal SUSY B-L model

We perform a study of the dark matter candidates of a constrained version of the minimal R-parity-conserving supersymmetric model with a gauged $U(1)_{B-L}$. It turns out that there are four additional candidates for dark matter in comparison to the MSSM: two kinds of neutralino, which either correspond to the gaugino of the $U(1)_{B-L}$ or to a fermionic bilepton, as well as "right-handed" CP-even and -odd sneutrinos. The correct dark matter relic density of the neutralinos can be obtained due to different mechanisms including new co-annihilation regions and resonances. The large additional Yukawa couplings required to break the $U(1)_{B-L}$ radiatively often lead to large annihilation cross sections for the sneutrinos. The correct treatment of gauge kinetic mixing is crucial to the success of some scenarios. All candidates are consistent with the exclusion limits of Xenon100.Comment: 45 pages, 22 figures; v2: extended discussion of direct detection cross section, matches published versio

Measuring co-authorship and networking-adjusted scientific impact

Appraisal of the scientific impact of researchers, teams and institutions with productivity and citation metrics has major repercussions. Funding and promotion of individuals and survival of teams and institutions depend on publications and citations. In this competitive environment, the number of authors per paper is increasing and apparently some co-authors don't satisfy authorship criteria. Listing of individual contributions is still sporadic and also open to manipulation. Metrics are needed to measure the networking intensity for a single scientist or group of scientists accounting for patterns of co-authorship. Here, I define I1 for a single scientist as the number of authors who appear in at least I1 papers of the specific scientist. For a group of scientists or institution, In is defined as the number of authors who appear in at least In papers that bear the affiliation of the group or institution. I1 depends on the number of papers authored Np. The power exponent R of the relationship between I1 and Np categorizes scientists as solitary (R>2.5), nuclear (R=2.25-2.5), networked (R=2-2.25), extensively networked (R=1.75-2) or collaborators (R<1.75). R may be used to adjust for co-authorship networking the citation impact of a scientist. In similarly provides a simple measure of the effective networking size to adjust the citation impact of groups or institutions. Empirical data are provided for single scientists and institutions for the proposed metrics. Cautious adoption of adjustments for co-authorship and networking in scientific appraisals may offer incentives for more accountable co-authorship behaviour in published articles.Comment: 25 pages, 5 figure