Abstract
We consider the tensor formulation of the nonlinear O(2) sigma model and its gauged version (the compact Abelian Higgs model), on a $D$-dimensional cubic lattice, and show that tensorial truncations are compatible with the general identities derived from the symmetries of these models. This means that the universal properties of these models can be reproduced with highly simplified formulations desirable for implementations with quantum computers or for quantum simulations experiments. We discuss the extensions to global non-Abelian symmetries, discrete symmetries and pure gauge Abelian models.
Highlights
We focus on two related examples with a continuous Abelian symmetry: the O(2) nonlinear sigma model and the compact Abelian Higgs model
In the case of the global symmetry previously discussed, we found that if the sum of the inserted charges in the full D-dimensional space-time volume is nonzero, there is a flow at the boundary clashing with Periodic boundary conditions (PBCs) or Open boundary conditions (OBCs) and the average can only be zero
We have discussed the way symmetries are implemented in tensor field theory (TFT) for two models with a continuous Abelian symmetry
Summary
There has been a lot interest for tensorial formulations of lattice models in the context of the renormalization group method [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. For theories with compact fields like the nonlinear sigma models and Wilson lattice gauge theories, the tensor reformulation relies on character expansions and is always discretized [7] This is suitable for quantum computations or quantum simulations [23,24,25]. In practical situations such as tensor renormalization group (TRG) calculations, truncations of infinite sums appearing in the TFT formulation of models with continuous symmetries are necessary. This can be achieved by discarding contributions to the partition function or observable averages that involve tensor indices larger than some cutoff value nmax. We summarize the results, provide an intuitive picture and emphasize the practical implications of the results
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