Laboratoire de Physique Théorique
Toulouse - UMR 5152

The investigation of strongly correlated systems is associated to many central problems in condensed matter and statistical physics, and must often be be performed via numerical approaches, due to the lack of reliable analytical approaches. Insight into these problems can nowadays also be gathered via quantum simulation, i.e., by engineering an experiment governed by a Hamiltonian of choice. This progress has created further interest in these models, making their theoretical study of even greater importance, as a beacon for the laboratory towards physically interesting regimes and scenarios. This talk will center on my investigations of strongly correlated systems relevant for experimental realizations with cold atom systems, which I perform via path integral Monte Carlo simulations : these approaches give unbiased equilibrium and ground-state results, as well as insight into out-of-equilibrium scenarios via simulated quench protocols.

After an introduction to the necessary topics, I will first discuss my results for cluster-forming bosonic systems of interest for Rydberg-dressed atom experiments. Here, the formation of particle clusters leads to a variety of equilibrium and out-of-equilibrium physical scenarios, including the formation of superglass phases, where glassy behavior coexists with superfluidity, as well as phase transitions between different types of supersolid states. Subsequently, I will discuss my results on long-range quantum spin systems, whose properties, especially concerning thermalization and dynamics, have been the object of various investigations in cold atom experiments. I determined the universal and non-universal critical properties of quantum Ising models with long-range spin-spin interactions, in regimes (such as the case of finite temperature) where only conjectures of uncertain applicability on these features existed, obtaining results of direct experimental interest.