Tensor Network Methods for the Driven-Dissipative Dynamics of Polariton Lattice Quantum Simulators

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Light matter based quantum simulation platforms such as polariton lattices and circuit QED systems have recently shown the ability to support stong many-body quantum correlations. Here, the strong correlations between light-matter particles lead to highly non-classical phenomena such as photon blockade, superfluid to Mott insulator phase transitions and non-linear topological physics. Numerical methods to understand these systems in one- and two- dimensions have mostly been restricted to mean field theories which are expected to break down in the limit of strong correlations. In this work, new methods based on tensor networks are developed to simulate driven dissipative many-body systems in the strongly correlated regime. These methods are based on matrix products states (MPS) for one-dimensional systems and projected entangled pair states (PEPS) for two-dimensional systems. It is expected that these new techniques will offer valuable insight into the dynamics of strongly correlated light-matter systems.