Consistent Application of Maximum Entropy to Quantum-Monte-Carlo Data

Bayesian statistics in the frame of the maximum entropy concept has widely been used for inferential problems, particularly, to infer dynamic properties of strongly correlated fermion systems from Quantum-Monte-Carlo (QMC) imaginary time data. In current applications, however, a consistent treatment of the error-covariance of the QMC data is missing. Here we present a closed Bayesian approach to account consistently for the QMC-data.Comment: 13 pages, RevTeX, 2 uuencoded PostScript figure

A discrete Hubbard-Stratonovich decomposition for general, fermionic two-body interactions

A scheme is presented to decompose the exponential of a two-body operator in a discrete sum over exponentials of one-body operators. This discrete decomposition can be used instead of the Hubbard-Stratonovich transformation in auxiliary-field quantum Monte-Carlo methods. As an illustration, the decomposition is applied to the Hubbard model, where it is equivalent to the discrete Hubbard-Stratonovich transformation introduced by Hirsch, and to the nuclear pairing Hamiltonian.Comment: 8 pages, includes 2 eps figures, to appear in Phys. Lett.

Orbital polarons versus itinerant e_g electrons in doped manganites

We study an effective one-dimensional (1D) orbital t-J model derived for strongly correlated e_g electrons in doped manganites. The ferromagnetic spin order at half filling is supported by orbital superexchange prop. to J which stabilizes orbital order with alternating x^2-y^2 and 3z^2-r^2 orbitals. In a doped system it competes with the kinetic energy prop. to t. When a single hole is doped to a half-filled chain, its motion is hindered and a localized orbital polaron is formed. An increasing doping generates either separated polarons or phase separation into hole-rich and hole-poor regions, and eventually polarizes the orbitals and gives a it metallic phase with occupied 3z^2-r^2 orbitals. This crossover, investigated by exact diagonalization at zero temperature, is demonstrated both by the behavior of correlation functions and by spectral properties, showing that the orbital chain with Ising superexchange is more classical and thus radically different from the 1D spin t-J model. At finite temperature we derive and investigate an effective 1D orbital model using a combination of exact diagonalization with classical Monte-Carlo for spin correlations. A competition between the antiferromagnetic and ferromagnetic spin order was established at half filling, and localized polarons were found for antiferromagnetic interactions at low hole doping. Finally, we clarify that the Jahn-Teller alternating potential stabilizes the orbital order with staggered orbitals, inducing the ferromagnetic spin order and enhancing the localized features in the excitation spectra. Implications of these findings for colossal magnetoresistance manganites are discussed.Comment: 19 pages, 20 figure

On the prevalence of radio-loud AGN in brightest cluster galaxies: implications for AGN heating of cooling flows

(Abridged) The prevalence of radio-loud AGN activity in present-day massive halos is determined using a sample of 625 nearby groups and clusters from the SDSS. Brightest group and cluster galaxies (BCGs) are more likely to host a radio-loud AGN than other galaxies of the same stellar mass (by less than a factor of two at a stellar mass of 5e11 M_sun, but over an order of magnitude below 1e11 M_sun). The distribution of radio luminosities for BCGs does not depend on stellar mass, however, and is similar to that of field galaxies of the same mass. Neither the radio-loud fraction nor the radio luminosity distribution of BCGs depends strongly on the cluster velocity dispersion. The radio-AGN fraction is also studied as a function of clustercentric distance: only within 0.2 r_200 do cluster galaxies exhibit an enhanced likelihood of radio-loud AGN activity, approaching that of the BCGs. The radio-loud AGN properties of both BCGs and non-BCGs can naturally be explained if this activity is fuelled by cooling from hot gas surrounding the galaxy. Using observational estimates of the mechanical output of the radio jets, the time-averaged energy output associated with recurrent radio source activity is estimated for all group/cluster galaxies. Within the cooling radius of the cluster, the radio-mode heating from the BCG dominates over that of all other galaxies combined. The scaling between total radio-AGN energy output and cluster velocity dispersion is considerably shallower than the sigma^4 scaling of the radiative cooling rate. Thus, unless either the mechanical-to-radio luminosity ratio or the efficiency of converting AGN mechanical energy into heating increases by 2-3 orders of magnitude between groups and rich clusters, radio-mode heating will not balance cooling in systems of all masses.Comment: Accepted for publication in MNRAS. LaTeX, 16 pages. Pages 6,7 and 8 contain colour figures. Revised to take into account referee's comments: addition of Sec 7.2, removal of Figure 2b, and other minor change

Accessing the dynamics of large many-particle systems using Stochastic Series Expansion

The Stochastic Series Expansion method (SSE) is a Quantum Monte Carlo (QMC) technique working directly in the imaginary time continuum and thus avoiding "Trotter discretization" errors. Using a non-local "operator-loop update" it allows treating large quantum mechanical systems of many thousand sites. In this paper we first give a comprehensive review on SSE and present benchmark calculations of SSE's scaling behavior with system size and inverse temperature, and compare it to the loop algorithm, whose scaling is known to be one of the best of all QMC methods. Finally we introduce a new and efficient algorithm to measure Green's functions and thus dynamical properties within SSE.Comment: 11 RevTeX pages including 7 figures and 5 table

X-ray Bright Active Galactic Nuclei in Massive Galaxy Clusters II: The Fraction of Galaxies Hosting Active Nuclei

We present a measurement of the fraction of cluster galaxies hosting X-ray bright Active Galactic Nuclei (AGN) as a function of clustercentric distance scaled in units of $r_{500}$. Our analysis employs high quality Chandra X-ray and Subaru optical imaging for 42 massive X-ray selected galaxy cluster fields spanning the redshift range of $0.2 < z < 0.7$. In total, our study involves 176 AGN with bright ($R <23$) optical counterparts above a $0.5-8.0$ keV flux limit of $10^{-14} \rm{erg} \ \rm{cm}^{-2} \ \rm{s}^{-1}$. When excluding central dominant galaxies from the calculation, we measure a cluster-galaxy AGN fraction in the central regions of the clusters that is $\sim 3$ times lower that the field value. This fraction increases with clustercentric distance before becoming consistent with the field at $\sim 2.5 r_{500}$. Our data exhibit similar radial trends to those observed for star formation and optically selected AGN in cluster member galaxies, both of which are also suppressed near cluster centers to a comparable extent. These results strongly support the idea that X-ray AGN activity and strong star formation are linked through their common dependence on available reservoirs of cold gas.Comment: 9 Pages, 4 Figures, accepted for publication in MNRAS, please contact Steven Ehlert ([email protected]) with any querie

X-ray bright active galactic nuclei in massive galaxy clusters III: New insights into the triggering mechanisms of cluster AGN

We present the results of a new analysis of the X-ray selected Active Galactic Nuclei (AGN) population in the vicinity of 135 of the most massive galaxy clusters in the redshift range of 0.2 < z < 0.9 observed with Chandra. With a sample of more than 11,000 X-ray point sources, we are able to measure, for the first time, evidence for evolution in the cluster AGN population beyond the expected evolution of field AGN. Our analysis shows that overall number density of cluster AGN scales with the cluster mass as $\sim M_{500}^{-1.2}$. There is no evidence for the overall number density of cluster member X-ray AGN depending on the cluster redshift in a manner different than field AGN, nor there is any evidence that the spatial distribution of cluster AGN (given in units of the cluster overdensity radius r_500) strongly depends on the cluster mass or redshift. The $M^{-1.2 \pm 0.7}$ scaling relation we measure is consistent with theoretical predictions of the galaxy merger rate in clusters, which is expected to scale with the cluster velocity dispersion, $\sigma$, as $\sim \sigma^{-3}$ or $\sim M^{-1}$. This consistency suggests that AGN in clusters may be predominantly triggered by galaxy mergers, a result that is further corroborated by visual inspection of Hubble images for 23 spectroscopically confirmed cluster member AGN in our sample. A merger-driven scenario for the triggering of X-ray AGN is not strongly favored by studies of field galaxies, however, suggesting that different mechanisms may be primarily responsible for the triggering of cluster and field X-ray AGN.Comment: 21 Pages, 8 figures, 5 tables. Submitted to MNRAS. Comments are welcome, and please request Steven Ehlert for higher resolution figure

Quasiparticle Dispersion of the 2D Hubbard Model: From an Insulator to a Metal

On the basis of Quantum-Monte-Carlo results the evolution of the spectral weight $A(\vec k, \omega)$ of the two-dimensional Hubbard model is studied from insulating to metallic behavior. As observed in recent photoemission experiments for cuprates, the electronic excitations display essentially doping-independent features: a quasiparticle-like dispersive narrow band of width of the order of the exchange interaction $J$ and a broad valence- and conduction-band background. The continuous evolution is traced back to one and the same many-body origin: the doping-dependent antiferromagnetic spin-spin correlation.Comment: 11 pages, REVtex, 4 figures (in uuencoded postscript format

Characterization of Mott-insulating and superfluid phases in the one-dimensional Bose--Hubbard model

We use strong-coupling perturbation theory, the variational cluster approach (VCA), and the dynamical density-matrix renormalization group (DDMRG) method to investigate static and dynamical properties of the one-dimensional Bose--Hubbard model in both the Mott-insulating and superfluid phases. From the von Neumann entanglement entropy we determine the central charge and the transition points for the first two Mott lobes. Our DMRG results for the ground-state energy, momentum distribution function, boson correlation function decay, Mott gap, and single particle-spectral function are reproduced very well by the strong-coupling expansion to fifth order, and by VCA with clusters up to 12 sites as long as the ratio between the hopping amplitude and on-site repulsion, t/U, is smaller than 0.15 and 0.25, respectively. In addition, in the superfluid phase VCA captures well the ground-state energy and the sound velocity of the linear phonon modes. This comparison provides an authoritative estimate for the range of applicability of these methods. In strong-coupling theory for the Mott phase, the dynamical structure factor is obtained from the solution of an effective single-particle problem with an attractive potential. The resulting resonances show up as double-peak structure close to the Brillouin zone boundary. These high-energy features also appear in the superfluid phase which is characterized by a pronounced phonon mode at small momenta and energies, as predicted by Bogoliubov and field theory. In one dimension, there are no traces of an amplitude mode in the dynamical single-particle and two-particle correlation functions.Comment: 15 pages, 12 figure