Multilevel Monte Carlo for quantum mechanics on a lattice

  title={Multilevel Monte Carlo for quantum mechanics on a lattice},
  author={Karl Jansen and Eike Hermann M{\"u}ller and Robert Scheichl},
Monte Carlo simulations of quantum field theories on a lattice become increasingly expensive as the continuum limit is approached since the cost per independent sample grows with a high power of the inverse lattice spacing. Simulations on fine lattices suffer from critical slowdown, the rapid growth of autocorrelations in the Markov chain with decreasing lattice spacing. This causes a strong increase in the number of lattice configurations that have to be generated to obtain statistically… Expand


Collective Monte Carlo updating for spin systems.
  • Wolff
  • Physics, Medicine
  • Physical review letters
  • 1989
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