September 15, 2014 to October 10, 2014
Nordita, Stockholm
Europe/Stockholm timezone

Recent Developments and Applications of the Auxiliary-Field Monte Carlo Method

Sep 16, 2014, 10:40 AM
FP41 (Nordita, Stockholm)


Nordita, Stockholm


Christopher Gilbreth


The auxiliary-field Monte Carlo (AFMC) method is a powerful technique to calculate thermal and ground-state properties of strongly correlated systems. In particular, it has been extensively applied to study the properties of nuclear and atomic systems. We discuss several recent developments and applications of the method to finite-size systems. (i) In finite systems, it is often necessary to use the canonical ensemble with fixed number of particles. However, the projection on an odd number of particles leads to a new sign problem at low temperatures that has severely limited the application of AFMC to such systems. We discuss a method to circumvent the odd-particle sign problem which allows accurate determination of the ground-state energy, and present its application to the calculation of nuclear pairing gaps from odd-even mass differences [1]. (ii) The level density is among the most important statistical nuclear properties, but its calculation in the presence of correlations is a difficult many-body problem. We discuss recent AFMC calculations of level densities in heavy nuclei. In particular, we present the first microscopic calculation of the collective enhancement factors, which describe the enhancement of level densities by collective states [2]. (iii) Low-temperature calculations require numerical stabilization of the long chains of matrix multiplications necessary to compute the propagator, and a corresponding stabilized method for particle-number projection. The latter is computationally expensive. We discuss an improved method of stabilizing canonical-ensemble calculations that exhibits better scaling and allows calculations for much larger systems [3]. (iv) Deformation is an important concept for the understanding of heavy nuclei. However, it is based on mean-field theory, which breaks rotational invariance, a cornerstone symmetry of finite nuclei. We discuss a method to analyze nuclear deformations at finite temperature using AFMC, which preserves the rotational invariance of the system [4]. In particular, we calculate the probability distribution of the quadrupole operator in heavy rare-earth nuclei, and show that it carries model-independent signatures of deformation. References: [1] A. Mukherjee and Y. Alhassid, Phys. Rev. Lett. 109, 032503 (2012). [2] C. Ozen, Y. Alhassid and H. Nakada, Phys. Rev. Lett. 110, 042502 (2013). [3] C. N. Gilbreth and Y. Alhassid, arXiv:1402.3585 (2014). [4] Y. Alhassid, C. N. Gilbreth and G. F. Bertsch, arXiv:1408.0081 (2014)

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