Three-dimensional finite temperature Z2 gauge theory with tensor network scheme

Yusuke Yoshimura

Jacek Dziarmaga

Loopy tensor networks exhibit internal correlations that often render their compression inefficient. We show that even local bond optimization can more effectively exploit locally available information about relevant loop correlations. By cutting a bond, we define a set of states whose linear dependence can be identified through a zero mode of the states' metric tensor and used to truncate the bond dimension. In the absence of an exact zero mode, a linear combination of a small number of the lowest modes can instead be optimized to provide the optimal approximation to a zero mode. The truncation does not require prior gauge fixing. The method is applied to the two-dimensional finite-temperature $Z_2$ lattice gauge theory, whose thermal-state purification is represented by an infinite projected entangled-pair state (iPEPS).

Yoshinobu Kuramashi, Yusuke Yoshimura

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 N σ = 4096 at the temporal extension of N τ = 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.

Jacques Bloch, Robert Lohmayer, Sophia Schweiss +1 more

Atis Yosprakob, Kouichi Okunishi

We perform a tensor renormalization group simulation of non-Abelian gauge theory in three dimensions using a formulation based on the `armillary sphere.' In this formulation, matrix indices are completely traced out, eliminating the degeneracy in the singular value spectrum of the initial tensor. We demonstrate the usefulness of this technique by computing the average plaquette at zero temperature and the Polyakov loop susceptibility at finite temperatures for 2+1D SU(2) and SU(3) gauge theories. The deconfinement transition is identified for both gauge groups, with the SU(2) case being consistent with previous Monte Carlo results.

Mari Carmen Bañuls, Krzysztof Cichy, J. I. Cirac +2 more