Quantum Monte Carlo Study of Strongly Correlated Electrons: Cellular Dynamical Mean-Field Theory

We study the Hubbard model using the Cellular Dynamical Mean-Field Theory (CDMFT) with quantum Monte Carlo (QMC) simulations. We present the algorithmic details of CDMFT with the Hirsch-Fye QMC method for the solution of the self-consistently embedded quantum cluster problem. We use the one- and two-dimensional half-filled Hubbard model to gauge the performance of CDMFT+QMC particularly for small clusters by comparing with the exact results and also with other quantum cluster methods. We calculate single-particle Green's functions and self-energies on small clusters to study their size dependence in one- and two-dimensions.Comment: 14 pages, 18 figure

Revisiting the Cooling Flow Problem in Galaxies, Groups, and Clusters of Galaxies

We present a study of 107 galaxies, groups, and clusters spanning ~3 orders of magnitude in mass, ~5 orders of magnitude in central galaxy star formation rate (SFR), ~4 orders of magnitude in the classical cooling rate (dM/dt) of the intracluster medium (ICM), and ~5 orders of magnitude in the central black hole accretion rate. For each system in this sample, we measure dM/dt using archival Chandra X-ray data and acquire the SFR and systematic uncertainty in the SFR by combining over 330 estimates from dozens of literature sources. With these data, we estimate the efficiency with which the ICM cools and forms stars, finding e_cool = SFR/(dM/dt) = 1.4 +/- 0.4% for systems with dM/dt > 30 Msun/yr. For these systems, we measure a slope in the SFR-dM/dt relation greater than unity, suggesting that the systems with the strongest cool cores are also cooling more efficiently. We propose that this may be related to, on average, higher black hole accretion rates in the strongest cool cores, which could influence the total amount (saturating near the Eddington rate) and dominant mode (mechanical vs radiative) of feedback. For systems with dM/dt < 30 Msun/yr, we find that the SFR and dM/dt are uncorrelated, and show that this is consistent with star formation being fueled at a low (but dominant) level by recycled ISM gas in these systems. We find an intrinsic log-normal scatter in SFR at fixed dM/dt of 0.52 +/- 0.06 dex, suggesting that cooling is tightly self-regulated over very long timescales, but can vary dramatically on short timescales. There is weak evidence that this scatter may be related to the feedback mechanism, with the scatter being minimized (~0.4 dex) in systems for which the mechanical feedback power is within a factor of two of the cooling luminosity.Comment: 16 pages, 10 figures, 6 tables. Submitted to ApJ. Comments welcome