### Speaker

Christopher Gilbreth

### Description

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)