Abstract
We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol, adapted to operate entirely at the level of fields. This strategy was applied in Ref.[1] to the much simpler case of a free boson, obtaining an excellent performance. Here we include an arbitrary self-interaction and treat it in the context of perturbation theory. A real space analogue of the Wilsonian effective action and its expansion in Feynman graphs is proposed. Using a λϕ4 theory for benchmark, we evaluate the order λ correction to the free energy. The results show a fast convergence with the bond dimension, implying that our algorithm captures well the effect of interaction on entanglement.
Highlights
We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions
The aim of this paper is to present a new framework for a real space renormalization group (RG) analysis of quantum field theories
After the maximal bond dimension is reached, they result from the factorization of the Boltzmann weights plus a truncation guided by the matrix Bn the associated fields is close to a delta function and, as discussed above, the Tensor Renormalization Group (TRG) protocol can deal with these objects
Summary
The aim of this paper is to present a new framework for a real space renormalization group (RG) analysis of quantum field theories. It will combine the main guidelines of a conventional particle physics approach to quantum field theory [63, 64] with the introduction of a classification of degrees of freedom based on entanglement. The main focus of study will be the partition function, whose RG analysis will be formulated in terms of fields x ∈ R. In the spirit of lattice field theory, the spacetime will be discretized. We will study a discretized version of this theory living on a square lattice. The field variables are assigned to the lattice links while the statistical or Boltzmann weights are carried by the vertices [2]
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