Tensor Network Simulations of Non-Abelian Lattice Gauge Theories

We present advanced Tensor Network methods for the study of non-Abelian Hamiltonian Lattice Gauge Theories, particularly addressing real-time dynamics and finite-density regimes. A novel dressed-site formalism allows for efficient truncation of gauge fields while preserving gauge invariance. This approach has been successfully applied to SU(2) Yang-Mills LGTs with dynamical matter, yielding the first observations of key in- and out-of-equilibrium features. In two dimensions, Tensor Network simulations uncover critical aspects of the phase diagram, including a liquid phase of quark-pair bound-state quasiparticles (baryons) [PhysRevResearch.6.033057]. In one dimension, we observe Quantum Many-Body (QMB) scarring dynamics, intimately connected to the non-Abelian nature of the theory [arXiv.2405.13112].