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We formulate the path integral of two- and three-flavor Wilson fermion in twodimensions as a multilayer Grassmann tensor network by the matrix productdecomposition. Thanks to this new description, the memory cost scaling isreduced from $\mathrm{O}(\mathrm{e}^{N_{f}})$ for the conventional constructionto $\mathrm{O}(N_{f})$. Based on this representation, we develop acoarse-graining algorithm where spatially or temporally adjacent Grassmanntensors are converted into a canonical form along a virtual direction before wecarry out the spacetime coarse-graining. Benchmarking with the latticeGross-Neveu model at finite density, we see that the Silver Blaze phenomenon inthe pressure and number density is captured with relatively small bonddimensions.

Matrix product decomposition for two- and three-flavor Wilson fermions: Benchmark results in the lattice Gross-Neveu model at finite density