Collective Monte Carlo updates through tensor network renormalization

 We will introduce a Metropolis-Hastings Markov chain for Boltzmann distributions of classical spin systems. It relies on approximate tensor network contractions to propose correlated collective updates at each step of the evolution. We will present benchmarks for various instances of the two-dimensional Ising model, and show that the Markov chain compares well with other Monte Carlo schemes such as the Metropolis or Wolff algorithm: equilibration times appear to be reduced by a factor that varies between 40 and 2000, depending on the model and the observable being monitored. Time permitting, extensions to three spatial dimensions and to other models will also be discussed. Joint work with Miguel Frías-Pérez, Michael Mariën, David Pérez García, and Mari Carmen Bañuls (arXiv:2104.13264).