# Tensor renormalization group in bosonic field theory

## TL;DR

This paper applies a tensor network algorithm with a novel SVD approach to compute the partition function of a free boson on a lattice, revealing fixed point structures and matching conformal field theory results in the massless limit.

## Contribution

It introduces a continuous matrix SVD for tensor networks, enabling highly accurate calculations of bosonic field theories on lattices.

## Key findings

- Emergence of a CDL fixed point structure
- Accurate reproduction of conformal field theory results
- Precise determination of the central charge in the massless limit

## Abstract

We compute the partition function of a massive free boson in a square lattice using a tensor network algorithm. We introduce a singular value decomposition (SVD) of continuous matrices that leads to very accurate numerical results. It is shown the emergence of a CDL fixed point structure. In the massless limit, we reproduce the results of conformal field theory including a precise value of the central charge.