Critical endpoint of (3+1)-dimensional finite density ℤ3 gauge-Higgs model with tensor renormalization group

Abstract

The critical endpoint of the (3+1)-dimensional ℤ3 gauge-Higgs model at finite density is determined by the tensor renormalization group method. This work is an extension of the previous one on the ℤ2 model. The vital difference between them is that the ℤ3 model suffers from the sign problem, while the ℤ2 model does not. We show that the tensor renormalization group method allows us to locate the critical endpoint for the ℤ3 gauge-Higgs model at finite density, regardless of the sign problem.

Entanglement and Rényi entropies of (1+1)-dimensional O(3) nonlinear sigma model with tensor renormalization group

“…We obtain the value of c = 1.97 (9), which is consistent with c = 2.04 (14) obtained by the MPS method in ref. [31].…”

“…We have calculated the entanglement and Rényi entropies for the (1+1)-dimensional O(3) NLSM under the condition ξ ≪ L using the tensor renormalization group method. The central charge obtained from the asymptotic scaling behavior of the entanglement entropy is c = 1.97 (9), which is consistent with c = 2.04 (14) previously obtained with the MPS method. We have also investigated the consistency between the entanglement entropy and the Rényi entropies.…”

“…In the past decade the tensor renormalization group (TRG) method, 1 which was originally proposed in the condensed matter physics [1], has been getting applied to the particle physics. Although the target models in the initial stage were restricted to the 2d ones, recent studies cover various four-dimensional (4d) models with the scalar, gauge and fermion fields [7,[10][11][12][13][14]. So far much attention has been paid to the sign-problem-free nature of the TRG method [3,[15][16][17][18][19][20][21][22][23][24].…”

A new technique to incorporate multiple fermion flavors in tensor renormalization group method for lattice gauge theories

“…A recent achievement of the TRG method is its application to gauge theory, in particular in the parameter regions that are not accessible to Monte Carlo methods due to the sign problem. Notable examples include the 2D gauge theories with a θ term [36][37][38], 2D SU(2) gauge-Higgs model [39], one-flavor Schwinger model [27,40,41], 2D QCD [42], 3D SU (2) gauge theory [43], 4D Z K gauge-Higgs models [44,45] and so on. Among these applications, gauge theories with matter fields are of particular importance since typically they are not exactly solvable.…”

GrassmannTN: A Python package for Grassmann tensor network computations

“…Most importantly, the partition function with fermionic or Grassmann degrees of freedom can be dealt with directly without the need to integrate the fermions out first [14,[21][22][23][24]. Recently, the TRG has been applied to gauge theories and strongly correlated fermionic systems [13,[24][25][26][27][28][29][30][31][32][33][34], which shows that it is a promising approach aside from the Monte Carlo methods.…”