Abstract
We apply a tensor network scheme to finite temperature Z2 gauge theory in 2+1 dimensions. Finite size scaling analysis with the spatial extension up to Nσ = 4096 at the temporal extension of Nτ = 2, 3, 5 allows us to determine the transition temperature and the critical exponent ν at high level of precision, which shows the consistency with the Svetitsky-Yaffe conjecture.
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T. Nishino and K. Okunishi, Corner transfer matrix renormalization group method, J. Phys. Soc. Jpn.65 (1996) 891.
N. Maeshima, Y. Hieida, Y. Akutsu, T. Nishino and K. Okunishi, Vertical density matrix algorithm: a higher dimensional numerical renormalization scheme based on the tensor product state ansatz, Phys. Rev.E 64 (2001) 016705 [cond-mat/0101360] [INSPIRE].
M. Levin and C.P. Nave, Tensor renormalization group approach to 2D classical lattice models, Phys. Rev. Lett.99 (2007) 120601 [cond-mat/0611687] [INSPIRE].
Z.-C. Gu and X.-G. Wen, Tensor-entanglement-filtering renormalization approach and symmetry protected topological order, Phys. Rev.B 80 (2009) 155131 [arXiv:0903.1069] [INSPIRE].
Y. Shimizu, Tensor renormalization group approach to a lattice boson model, Mod. Phys. Lett.A 27 (2012) 1250035 [INSPIRE].
Y. Shimizu and Y. Kuramashi, Grassmann tensor renormalization group approach to one-flavor lattice Schwinger model, Phys. Rev.D 90 (2014) 014508 [arXiv:1403.0642] [INSPIRE].
Z.-C. Gu, F. Verstraete and X.-G. Wen, Grassmann tensor network states and its renormalization for strongly correlated fermionic and bosonic states, arXiv:1004.2563 [INSPIRE].
Z.-C. Gu, Efficient simulation of Grassmann tensor product states, Phys. Rev.B 88 (2013) 115139 [arXiv:1109.4470] [INSPIRE].
Y. Shimizu and Y. Kuramashi, Critical behavior of the lattice Schwinger model with a topological term at θ = π using the Grassmann tensor renormalization group, Phys. Rev.D 90 (2014) 074503 [arXiv:1408.0897] [INSPIRE].
Y. Shimizu and Y. Kuramashi, Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion, Phys. Rev.D 97 (2018) 034502 [arXiv:1712.07808] [INSPIRE].
S. Takeda and Y. Yoshimura, Grassmann tensor renormalization group for the one-flavor lattice Gross-Neveu model with finite chemical potential, Prog. Theor. Exp. Phys.2015 (2015) 043B01.
D. Kadoh, Y. Kuramashi, Y. Nakamura, R. Sakai, S. Takeda and Y. Yoshimura, Tensor network formulation for two-dimensional lattice N = 1 Wess-Zumino model, JHEP03 (2018) 141 [arXiv:1801.04183] [INSPIRE].
R. Sakai, S. Takeda and Y. Yoshimura, Higher order tensor renormalization group for relativistic fermion systems, Prog. Theor. Exp. Phys.2017 (2017) 063B07 [arXiv:1705.07764] [INSPIRE].
Y. Yoshimura, Y. Kuramashi, Y. Nakamura, S. Takeda and R. Sakai, Calculation of fermionic Green functions with Grassmann higher-order tensor renormalization group, Phys. Rev.D 97 (2018) 054511 [arXiv:1711.08121] [INSPIRE].
Y. Liu et al., Exact blocking formulas for spin and gauge models, Phys. Rev.D 88 (2013) 056005 [arXiv:1307.6543] [INSPIRE].
B. Dittrich, F.C. Eckert and M. Martin-Benito, Coarse graining methods for spin net and spin foam models, New J. Phys.14 (2012) 035008 [arXiv:1109.4927] [INSPIRE].
B. Dittrich and F.C. Eckert, Towards computational insights into the large-scale structure of spin foams, J. Phys. Conf. Ser.360 (2012) 012004 [arXiv:1111.0967] [INSPIRE].
B. Dittrich, S. Mizera and S. Steinhaus, Decorated tensor network renormalization for lattice gauge theories and spin foam models, New J. Phys.18 (2016) 053009 [arXiv:1409.2407] [INSPIRE].
M. Caselle and M. Hasenbusch, Deconfinement transition and dimensional crossover in the 3D gauge Ising model, Nucl. Phys.B 470 (1996) 435 [hep-lat/9511015] [INSPIRE].
B. Svetitsky and L.G. Yaffe, Critical behavior at finite temperature confinement transitions, Nucl. Phys.B 210 (1982) 423 [INSPIRE].
Z.Y. Xie, J. Chen, M.P. Qin, J.W. Zhu, L.P. Yang and T. Xiang, Coarse-graining renormalization by higher-order singular value decomposition, Phys. Rev.B 86 (2012) 045139.
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ArXiv ePrint: 1808.08025
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Kuramashi, Y., Yoshimura, Y. Three-dimensional finite temperature Z2 gauge theory with tensor network scheme. J. High Energ. Phys. 2019, 23 (2019). https://doi.org/10.1007/JHEP08(2019)023
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DOI: https://doi.org/10.1007/JHEP08(2019)023