Quantum Monte Carlo (QMC) simulations of many body fermionic systems are considerably complicated by the well known sign problem [1]. Although very accurate approximation schemes have been developed for the calculation of static properties, like structure functions and energy, the possibility of extending such methodologies to the investigation of dynamical properties is still largely unexplored [2].
Recently, a number of innovative QMC methods have been conceived which map the imaginary time evolution into a random walk in the abstract manifold of Slater determinants. In such approaches the sign problem is not circumvented and still requires approximations, but emerges in a different - and hopefully easier to handle - way. We have focused on the phaseless auxiliary Fields QMC method (AFQMC), developed by Shiwei Zhang[3]. Generalizing the formal manipulations suggested by Assaad et al. [4], we propose a practical scheme to evaluate dynamic correlation functions in imaginary time, giving access to the study of excitations and response functions of interacting fermionic systems.
We have explored systematically the effects of the phaseless approximation, underlying the AFQMC technique and its dynamical generalization, via the study of exactly solvable simple models, comparing AFQMC predictions with exact solutions. We will present also results about a two-dimensional electron liquid, providing comparisons with other QMC techniques.

In collaboration with: D.E.Galli, S. Moroni and E.Vitali

REFERENCES:

[1] R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill (1965)
[2] M. Nava, D. Galli, S. Moroni and E. Vitali: arXiv:1302.1799 (2013)
[3] S. Zhang: 'Quantum Monte Carlo Methods for Strongly Correlated Electron Systems', in Theoretical Methods for Strongly Correlated Electron Systems, Springer Verlag (2003)
[4] M. Feldbacher and F. F. Assaad: Phys. Rev. B 63, 073105 (2001)

Network immunization against failures and epidemic spreading can be written as a constrained optimization problem, in which the constraints are fixed-point equations for some local (node or edge) variables describing the stationary state of the dynamics. I will show how the cavity method, and message-passing techniques, can be used to study this problem and design efficient algorithms on large networks.

Turning flocks of starlings are a paradigm for a synchronized, rapid change of direction in moving animal groups. The efficiency of the information transport during such a collective change of state is the key factor to prevent cohesion loss and preserve robustness. However, the precise mechanism by which natural groups achieve such efficiency is currently not fully understood. I will present an experimental and theoretical study of starlings flocks undergoing collective turns in which we analyze how the turning decision spreads across the flock [1]. We find sound-like propagation with no damping of information. This is in contrast with standard theories of collective animal behavior based on alignment, which predict a much slower, diffusive spread of information. We propose a novel theory for propagation of orientation in flocks whose key ingredient is the existence of a conserved spin current generated by the gauge symmetry of the system. The theory falls in the same dynamical universality class of superfluid transport in liquid helium, naturally explaining the dissipationless propagating mode observed in turning flocks. Superfluidity also provides a quantitative prediction for the speed of propagation of the information, according to which transport must be swifter the stronger the group's orientational order. This is confirmed by the experimental data. The link between strong order and efficient decision-making required by superfluidity may be the adaptive drive for the high degree of behavioral polarization observed in many living groups.

[1] arXiv:1303.7097, arXiv:1305.1495

In collaboration with: Andrea Cavagna, Irene Giardina, Alessandro Attanasi, Lorenzo Del Castello, Tomas S. Grigera, Stefania Melillo, Leonardo Parisi, Oliver Pohl, Edward Shen, Massimiliano Viale

I will introduce a statistical mechanic model of a network able to exhibit multitasking capabilities. In addition to their relevance in artificial intelligence, these models are increasingly important in immunology, where stored patterns represent strategies to fight pathogens and nodes represent lymphocyte clones. They allow us to understand the crucial ability of the immune system to respond simultaneously to multiple distinct antigen invasions.

We describe a population of individuals carrying one of the two possible variants of a gene (alleles). The population is subdivided into groups (demes) living on a fully connected graph, and individuals are allowed to migrate from one deme to another. While the stochastic dynamics (genetic drift) of each deme tends to fix one allele and make it present in all individuals of the deme, a deterministic force favours rare alleles (balancing selection). We investigate the influence of population subdivision on the mean time required by the population to fix one of the two alleles: this fixation time shows an unexpected behaviour as a function of the migration rate, which we rationalized within our approach.