Hamiltonian approaches to the physics of strongly correlated many body quantum- systems, focus on gauge theories

Many body quantum systems are notoriously hard. Exact physical predictions often require exponential resources, and approximate methods such as Monte
Carlo simulations, can only be used in some scenarios (at equilibrium for sign-problem free models).

Here I introduce two complementary sets of ideas both aiming to address and characterise many body quantum systems. One of them allows to perform
approximate Hamiltonian numerical simulations of many body systems with polynomial resources both at equilibrium and out-of-equilibrium, and is based
on expressing the many body wave function as a tensor network. The other is based on the idea that a quantum computer could help addressing the exponential complexity of quantum many body systems. While we still do not have a proper quantum computer, highly controllable quantum systems are already available in the labs. These systems can be used as "quantum simulators", to solve specific problems in quantum many body physics.

I will explain, in this context, my recent works that aim to use both strategies to characterise the strongly interacting regime of lattice gauge theories.

References on tensor network
arXiv:1405.4811
arXiv:1007.4145

References on quantum simulations
arXiv:1601.03303
arXiv:1211.2704
arXiv:1205.0496