Table 1 Dressed site Hilbert space dimensions

From: Tensor networks for lattice gauge theories beyond one dimension

ℓ

d

 

(2 + 1)-dimensions

(3 + 1)-dimensions

 

U(1)

SU(2)

SU(3)

U(1)

SU(2)

SU(3)

1

35

30

164

267

178

3096

2

165

168

752

3437

3670

52,476

3

455

600

3738

18,487

35,280

813,438

4

969

1650

19,878

64,953

214,958

17,490,134

5

1771

3822

43,698

177,155

967,466

69,232,482

6

2925

7840

82,128

408,421

3,509,062

228,461,186

7

4495

14,688

212,496

835,311

10,828,494

1,245,755,754

8

6545

25,650

333,538

1,561,841

29,473,038

2,782,999,996

  1. For increasing number ℓ of allowed electric energy density levels, the corresponding dimensions d in some 2- and 3-dimensional paradigmatic LGTs with dynamical matter and gauge groups U(1), SU(2), and SU(3) are shown.
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