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Tensor Renormalization Group for fermions

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arxiv 2401.08542 v1 pith:6OV3JHSK submitted 2024-01-16 hep-lat cond-mat.stat-mechquant-ph

classification hep-latcond-mat.stat-mechquant-ph
keywords fermionstensorapplieddimensionsgrassmanngroupmethodsmodels
verification ladder T0 review T1 audit T2 compute T3 formal
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We review the basic ideas of the Tensor Renormalization Group method and show how they can be applied for lattice field theory models involving relativistic fermions and Grassmann variables in arbitrary dimensions. We discuss recent progress for entanglement filtering, loop optimization, bond-weighting techniques and matrix product decompositions for Grassmann tensor networks. The new methods are tested with two-dimensional Wilson--Majorana fermions and multi-flavor Gross--Neveu models. We show that the methods can also be applied to the fermionic Hubbard model in 1+1 and 2+1 dimensions.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group

    hep-lat 2026-02 conditional novelty 6.0 of 10

    For one-flavor Gross-Neveu-Wilson fermions, the Aoki phase is bounded by c=1/2 Ising critical lines and terminates at strong coupling, while c=1 lines separate topological and trivial insulators.

  2. Roughening and dynamics of an electric flux string in a (2+1)D lattice gauge theory

    hep-lat 2025-05 conditional novelty 5.0 of 10

    Numerical MPS simulations confirm static roughening signatures in a 2+1D Z2 gauge theory and show that after a local quench the entanglement entropy grows linearly in the roughening region, consistent with a massless ...

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