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).