Quantum Field Theories with Tensor Renormalization Group

TL;DR

This paper discusses recent advancements in applying tensor renormalization group methods to quantum field theories, demonstrating its effectiveness in analyzing phase transitions and avoiding the sign problem in complex models.

Contribution

The paper introduces the application of tensor renormalization group techniques to various quantum field theories, including scalar, fermion, and gauge theories, in multiple dimensions.

Findings

TRG method successfully analyzes phase transitions in complex models.

TRG is free from the sign problem in practical calculations.

Applicable to four-dimensional quantum field theories.

Abstract

We report recent progress on the application of the tensor renormalization group (TRG) to quantum field theories pursued by the Tsukuba group. We explain how to treat the scalar, fermion, and gauge theories with the TRG method presenting the results for the phase transitions in the (3+1)-dimensional ((3+1)$d$) complex $\phi^4$ theory at finite density, (1+1)$d$ pure U(1) lattice gauge theory with a $\theta$ term, (3+1)$d$ Nambu--Jona-Lasinio model at finite density and (1+1)$d$ and (2+1)$d$ Hubbard models at an arbitrary chemical potential. It is demonstrated that the TRG method is free from the sign problem in practical calculations and applicable to the four-dimensional models.