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Matrix product decomposition for two- and three-flavor Wilson fermions: Benchmark results in the lattice Gross-Neveu model at finite density
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abstract
We formulate the path integral of two- and three-flavor Wilson fermion in two dimensions as a multilayer Grassmann tensor network by the matrix product decomposition. Thanks to this new description, the memory cost scaling is reduced from $\mathrm{O}(\mathrm{e}^{N_{f}})$ for the conventional construction to $\mathrm{O}(N_{f})$. Based on this representation, we develop a coarse-graining algorithm where spatially or temporally adjacent Grassmann tensors are converted into a canonical form along a virtual direction before we carry out the spacetime coarse-graining. Benchmarking with the lattice Gross-Neveu model at finite density, we see that the Silver Blaze phenomenon in the pressure and number density is captured with relatively small bond dimensions.
Forward citations
Cited by 2 Pith papers
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Toward tensor renormalization group study of lattice QCD
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