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arXiv:2304.01473 · Physical review. D/Physical review. D.

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

Shinichiro Akiyama

Published Aug 30, 2023• 6 citations
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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.

DOI
10.1103/physrevd.108.034514

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We present a comprehensive tensor network study of staggered, Wilson, and twisted mass fermions in the Hamiltonian formulation, using the massive two-flavor Schwinger model as a benchmark. Particular emphasis is placed on twisted mass fermions, whose properties in this context have not been systematically explored before. We confirm the expected O ( a ) improvement in the free theory and observe that this improvement persists in the interacting case. By leveraging an electric-field-based method for mass renormalization, we reliably tune to maximal twist and establish the method’s applicability in the two-flavor model. Once mass renormalization is included, the pion mass exhibits rapid convergence to the continuum limit. Finite-volume effects are addressed using two complementary approaches: dispersion relation fits and finite-volume scaling. Our results show excellent agreement with semiclassical predictions and reveal a milder volume dependence for twisted mass fermions compared to staggered and Wilson discretizations. In addition, we observe clear isospin-breaking effects, suggesting intriguing parallels with lattice QCD. These findings highlight the advantages of twisted mass fermions for Hamiltonian simulations and motivate their further exploration—particularly in view of future applications to higher-dimensional lattice gauge theories.