1. Quantum physics in optical lattices
Since the extraordinary achievement of Bose-Einstein condensation in dilute atomic ensembles, ultra-cold gases have emerged as a fascinating playground for testing and
enlarging the present knowledge in quantum physics at atomic scale. Moreover, over the last few years, the availability of tuneable interactions in such systems is opening the door to a whole new realm of novel physics.
The present project aims to explore quantum phases in ultra-cold atoms confined in
optical lattices. Initially, we are going to study and discuss the most significant achievements lately reported in literature, understanding as deeply as possible the theoretical aspects behind this fascinating physics. After having reviewed the
subject’s state-of-the-art, it is proposed a research work focus on soft-core and long-range interacting bosons confined in low-dimensional optical lattices. For these
systems we mean to characterise at finite and zero temperature quantum phases such as supersolidity (i.e. a solid phase with non-zero superfluid flow) and quantum glass as well. Such exotic phases have recently attracted the interest of many experimental
groups around the world, making therefore the present theoretical research as a possible support to experiments in the near future.
- J. I. Cirac, and P. Zoller, “Goals and opportunities in quantum simulation”, Nature Physics volume 8 page 264266 (2012).
- F. Cinti, T. Macrì, W. Lechner, G. Pupillo, and T. Pohl, “Defect-induced
supersolidity with soft-core bosons”, Nature Communications volume 5 article number 3235 (2014).
2. Diagrammatic Quantum Monte Carlo for strongly correlated systems
With the rapid increase of computational capabilities, the continued development of numerical techniques has become an indispensable tool for theoretical physics. This
has tremendously advanced our understanding of many-body problems, which often are unapproachable via simplified analytical descriptions. One such technique is the
worm algorithm for quantum Monte Carlo simulations, which has enabled exact solutions to interacting boson problems.
In the present proposal, We suggest two different lines of study. In the first case we plan to further extend the scope of the worm algorithm including the possibility to
calculate n-body Greens functions as well as feasible sampling methods for multi-species boson systems. About the second part, we propose to extend these numerical approaches to systems made up of fermions. In particular, while standard Monte
Carlo methods are inapplicable due to the well-known sign problem, recent developments suggest that so-called diagrammatic Monte Carlo techniques could
provide a promising approach for certain problems. Starting from implementat ions for specific situations, we aim to extend such techniques to a wider class of fermionic and spin systems.
- W. Krauth, “Algorithms and Computations”, Oxford (2006).
- D. Ceperley, “Path integral in the theory of condensed helium”, Review of Modern Physics volume 67 page 279 (1995).
- M. Boninsegni, N. Prokof’ev, and B. Svistunov, “Worm algorithm and
diagrammatic Monte Carlo: A new approach to continuous-space path integral Monte Carlo simulations” Physical Review E volume 74 page 036701 (2006).
3. Vector and chiral spin liquid phases in type-II multiferroics
The ability to precisely control the external- field response of novel materials forms the basis for numerous technological applications, such that its understanding and
further development constitutes an important aspect of condensed matter physics and materials science. A particularly promising example are so-called multiferroics
materials, which can be simultaneously ferromagnetic (spins) and ferroelectric (charges). These fascinating materials are potentially candidates for technological applications as magnetoelectric sensing or current-free electric control of magnetic
memories.
Here we are interested to study the physics of type-II multiferroics. In this case the geometric frustration and/or competing magnetic interactions seem to play a key role. Using computational as well as analytical approaches, we plan to investigate
appropriate order parameters such as the vector/scalar chirality (i.e. spin current with spiral/helical order) at finite and zero temperature. These investigations are geared
towards the ambitious long-term goal of devising practical ways for “designing” multiferroic materials, with well defined and selectable properties.
- S. W. Cheong, and M. Mostovoy, “Multiferroics: a magnetic twist for ferroelectricity”, Nature materials, volume 6 page 13 (2007).