The Use of Neural Networks to Solve the Sign Problem in Physical Models

The possibility of taming the sign problem, which arises in the study of fermionic systems with finite chemical potential, with the use of algorithms of neural networks is examined. A solution to the sign problem is crucial for current research in condensed matter physics and the physics of high-density quark–gluon plasma (a new state of matter to be studied at the FAIR and NICA accelerators, which are under construction). In the proposed approach, trained neural networks roughly reproduce Lefschetz thimbles: manifolds in complex space, where the imaginary part of the action is constant. It is demonstrated that a trained network speeds up (compared to the common gradient flow algorithm) substantially the construction of the integration manifold in complex space. It is also shown that fluctuations of the imaginary part of the action on the approximate manifold defined by the neural network are still substantially smaller than in the common reweighting method.