Evading the sign problem in random matrix simulations

Understand

We show how the sign problem occurring in dynamical simulations of random matrices at nonzero chemical potential can be avoided by judiciously combining matrices into subsets.

• For each subset the sum of fermionic determinants is real and positive such that importance sampling can be used in Monte Carlo simulations.
• The number of matrices per subset is proportional to the matrix dimension.
• We measure the chiral condensate and observe that the statistical error is independent of the chemical potential and grows linearly with the matrix dimension, which contrasts strongly with its exponential growth in reweighting methods.