Higher-order tensor renormalization group for relativistic fermion systems

Abstract

We apply the higher order tensor renormalization group to two and three dimensional relativistic fermion systems on the lattice. In order to perform a coarse-graining of tensor networks including Grassmann variables, we introduce Grassmann higher order tensor renormalization group. We test the validity of the new algorithm by comparing its results with those of exact or previous methods.

Investigation of Complex ϕ4 Theory at Finite Density in Two Dimensions Using TRG

“…So a development of this approach could lead to deep understanding of quantum field theories that suffer from the sign problem such as QCD at finite chemical potential, finite θ angle, chiral gauge theories and SUSY theories. Although the TRG algorithm has been already introduced into the research of lattice quantum field theories [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], further studies are desirable to confirm if the TRG properly works for theories with a severe sign problem.…”

Phase transition of four-dimensional Ising model with higher-order tensor renormalization group

“…One of attractive features in TRG and HOTRG is that we are allowed to directly study the thermodynamic properties; we can systematically increase the system size by repeating the coarse-graining steps in the algorithms. Although earlier studies with HOTRG are restricted to two-and three-dimensional systems [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55], including the three-dimensional classical Ising model [40], the algorithm itself is readily extended to a four-dimensional lattice. In this paper, we employ the HOTRG method to investigate the phase transition of the classical Ising model on the four-dimensional hypercube.…”

Tensor network formulation for two-dimensional lattice $$ \mathcal{N} $$ = 1 Wess-Zumino model

“…[38], and the Grassmann version was also proposed in ref. [39]. In this way one can in principle go this direction; however, the computational cost could be severe.…”