Ettore Vitali- Università degli Studi di Milano #
Novel Quantum Monte Carlo techniques for the study of dynamical properties of many-body Fermi systems #
Quantum Monte Carlo (QMC) techniques have become very powerful tools providing deep
insight into the
physical behaviour of strongly correlated systems. As far as equilibrium properties
of bosonic
systems are concerned, nowadays QMC simulations are able to provide "exact"
predictions.
Ordinary matter is made of fermions and dynamical properties hide plenty of physical
informations:
if one could ever achieve the accuracy that is now currently available for the
equilibrium
behavior of bosonic models, the importance for Condensed Matter Physics would be
outstanding.
For Fermi systems, it is very interesting to study approaches different from the
traditional ones
(fixed node), which may hopefully help in facing the severe challenge due to the
famous sign problem.
Here we address two novel methodologies to study dynamical properties of Fermi systems.
One relies on bosonic imaginary-time correlation functions, providing fermionic
eigenstates
as excitations over the bosonic ground state in a bigger Hilbert space, not imposing
quantum statistics [1,2]; such approach requires to pay the fee of inverting Laplace
transform in ill-posed
conditions. We have faced such a problem via the GIFT methodology [3]. Within this
approach,
we have studied the equation of state, the magnetic properties and the low energy
excitations of
two-dimensional 3He [2,4]. We have been able to extract for the first time the zero
sound mode from
ab-initio calculations, finding good agreement with experiments [5]. In principle
this methodology
provides "exact" results for energies and their derivatives; it gives access also to
a variational
estimation of dynamic structure factors. The main difficulty concernes the
extrapolation to the
thermodynamic limit.
The second approach relies on a phaseless fermionic Auxiliary-Fields QMC algorithm [6].
This method is based on a random walk taking place in the Slater Determinants space,
authomatically taking into account Fermi statistics; in a "Diffusion Monte Carlo"
strategy,
the sign approximation is translated into a non-local and somehow weaker condition,
involving only
the overlap of one Determinant on a given guiding function, resembling the typical
importance sampling
recypes. From a formal point of view the method relies on the Hubbard-Stratonovich
transformation.
We have preliminary results for dynamical properties of a three-dimensional jellium
model.
<br/>
<br/>

References:
</br>
[1] G. Carleo, S. Moroni, F. Becca, and S. Baroni, Phys. Rev. B 83, 060411 (2011).
</br>
[2] M. Nava, E. Vitali, A. Motta, D.E. Galli, and S. Moroni, arXiv:1103.0915.
</br>
[3] E. Vitali, M. Rossi, L. Reatto, and D.E. Galli, Phys. Rev. B 82, 174510 (2010).
</br>
[4] M. Nava, D.E. Galli, S. Moroni, and E. Vitali, in preparation.
</br>
[5] H. Godfrin, M. Meschke, H.J. Lauter, A. Sultan, H.M. Bohm, E. Krotscheck, and M.
Panholzer, Nature 483, 576 (2012).
</br>
[6] M. Suewattana, W. Purwanto, S. Zhang, H. Krakauer, and E.J. Walter, Phys. Rev. B
75, 245123 (2007).