A new technique to incorporate multiple fermion flavors in tensor renormalization group method for lattice gauge theories
We propose a new technique to incorporate multiple fermion flavors in the tensor renormalization group method for lattice gauge theories, where fermions are treated by the Grassmann tensor network formalism. The basic idea is to separate the site tensor into multiple layers associated with each flav...
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Zusammenfassung: | We propose a new technique to incorporate multiple fermion flavors in the
tensor renormalization group method for lattice gauge theories, where fermions
are treated by the Grassmann tensor network formalism. The basic idea is to
separate the site tensor into multiple layers associated with each flavor and
to introduce the gauge field in each layer as replicas, which are all
identified later. This formulation, after introducing an appropriate
compression scheme in the network, enables us to reduce the size of the initial
tensor with high efficiency compared with a naive implementation. The
usefulness of this formulation is demonstrated by investigating the chiral
phase transition and the Silver Blaze phenomenon in 2D Abelian gauge theories
with $N_{\rm f}$ flavors of Wilson fermions up to $N_{\rm f}=4$. |
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DOI: | 10.48550/arxiv.2309.01422 |