Hybrid Monte Carlo on Lefschetz Thimbles -- A study of the residual sign problem

Understand

We consider a hybrid Monte Carlo algorithm which is applicable to lattice theories defined on Lefschetz thimbles.

• In the algorithm, any point (field configuration) on a thimble is parametrized uniquely by the flow-direction and the flow-time defined at a certain asymptotic region close to the critical point, and it is generated by solving the gradient flow equation downward.
• The associated complete set of tangent vectors is also generated in the same manner.
• Molecular dynamics is then formulated as a constrained dynamical system, where the equations of motion with Lagrange multipliers are solved by the second-order constraint-preserving symmetric integrator.