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Based on the Lefschetz thimble formulation of path-integration, we analyzethe (0+1) dimensional Thirring model at finite chemical potentials and performhybrid Monte Carlo (HMC) simulations. We adopt the lattice action defined withthe staggered fermion and a compact link field for the auxiliary vector field.We firstly locate the critical points (saddle points) of the gradient flowswithin the subspace of time-independent (complex) link field, and study thethiemble structure and the Stokes phenomenon to identify the thimbles whichcontribute to the path-integral. Then, we perform HMC simulations on the singledominant thimble and compare the results to the exact solution. The numericalresults are in agreement with the exact ones in small and large chemicalpotential regions, while they show some deviation in the crossover region inthe chemical potential. We also comment on the necessity of the contributionsfrom multiple thimbles in the crossover region.

Application of the Lefschetz thimble formulation to the (0+1) dim. Thirring model at finite density