We introduce a novel operator renormalization-group method. This is a new and more powerful variant of the t expansion combining that method with the real-space renormalization-group approach. The aim is to extract infinite-volume physics at t\ensuremath{\rightarrow}\ensuremath{\infty} from calculations of only a few powers of t. Good results are obtained for the (1+1)-dimensional Ising model. The method readily generalizes to higher-dimensional spin theories and to a gauge-invariant treatment of gauge theories. These theories will require greater computational power.We introduce a novel operator renormalization-group method. This is a new and more powerful variant of the t expansion combining that method with the real-space renormalization-group approach. The aim is to extract infinite-volume physics at t\ensuremath{\rightarrow}\ensuremath{\infty} from calculations of only a few powers of t. Good results are obtained for the (1+1)-dimensional Ising model. The method readily generalizes to higher-dimensional spin theories and to a gauge-invariant treatment of gauge theories. These theories will require greater computational power.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsNov 15, 19886 citations

Quantum Field Theories with Tensor Renormalization Group

Shinichiro Akiyama, Y. Kuramashi, Yusuke Yoshimura

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.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.

arXiv:2111.04240International Symposium on Lattice Field Theory (LATTICE)May 16, 20224 citations

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.