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The corner transfer matrix renormalization group (CTMRG) algorithm has beenextensively used to investigate both classical and quantum two-dimensional (2D)lattice models. The convergence of the algorithm can strongly vary from modelto model depending on the underlying geometry and symmetries, and the presenceof algebraic correlations. An important factor in the convergence of thealgorithm is the lattice symmetry, which can be broken due to the necessity ofmapping the problem onto the square lattice. We propose a variant of the CTMRGalgorithm, designed for models with $C_3$-symmetry, which we apply to theconceptually simple yet numerically challenging problem of the triangularlattice Ising antiferromagnet in a field, at zero and low temperatures. Westudy how the finite-temperature three-state Potts critical line in this modelapproaches the ground-state Kosterlitz-Thouless transition driven by a reducedfield ($h/T$). In this particular instance, we show that the $C_3$-symmetricCTMRG leads to much more precise results than both existing results from exactdiagonalization of transfer matrices and Monte Carlo.

Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm