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Using tensor network methods, we perform finite-size scaling analysis tostudy the parameter-induced phase transitions of two-dimensional deformedAffleck-Kennedy-Lieb-Tasaki states. We use higher-order tensor renormalizationgroup method to evaluate the moments and the correlations. Then, the criticalpoint and critical exponents are determined simultaneously by collapsing thedata. Alternatively, the crossing points of the dimensionless ratios are usedto determine the critical point, and the scaling at the critical point is usedto determine the critical exponents. For the transition between the disorderedAKLT phase and the ferromagnetic ordered phase, we demonstrate that both thecritical point and the exponents can be determined accurately. Furthermore, thevalues of the exponents confirm that the AKLT-FM transition belongs to the 2DIsing universality class. We also investigate theBerezinskii-Kosterlitz-Thouless transition from the AKLT phase to the criticalXY phase. In this case we show that the critical point can be located by thecrossing point of the correlation ratio.

Finite-size scaling analysis of two-dimensional deformed Affleck-Kennedy-Lieb-Tasaki states