Collective Monte Carlo updates through tensor network renormalization

Understand

We 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 present benchmarks for a wide variety of instances of the two-dimensional Ising model, including ferromagnetic, antiferromagnetic, (fully) frustrated and Edwards-Anderson spin glass cases, and we show that, with modest computational effort, our Markov chain achieves sizeable acceptance rates, even in the vicinity of critical points.
• In each of the situations we have considered, 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.