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

Abstract

Using tensor network methods, we perform finite-size scaling analysis to study the parameter-induced phase transitions of two-dimensional deformed Affleck-Kennedy-Lieb-Tasaki states. We use higher-order tensor renormalization group method to evaluate the moments and the correlations. Then, the critical point and critical exponents are determined simultaneously by collapsing the data. Alternatively, the crossing points of the dimensionless ratios are used to determine the critical point, and the scaling at the critical point is used to determine the critical exponents. For the transition between the disordered AKLT phase and the ferromagnetic ordered phase, we demonstrate that both the critical point and the exponents can be determined accurately. Furthermore, the values of the exponents confirm that the AKLT-FM transition belongs to the 2D Ising universality class. We also investigate the Berezinskii-Kosterlitz-Thouless transition from the AKLT phase to the critical XY phase. In this case we show that the critical point can be located by the crossing point of the correlation ratio.

Tensor network calculation of the logarithmic correction exponent in the XY model

“…In the Ising and Potts models, the HOTRG method was also used to obtain the density of the LY zeros from the discontinuity of magnetization [28]. While tensor network methods have been actively applied to study phase transitions in classical and quantum systems [29], including the BKT transitions [30][31][32][33][34][35][36][37], the computation of the first LY zero in the XY model has not been studied with TRG yet. It still remains unclear whether or not a TRG-based method such as HOTRG allows enough accuracy to characterize such delicate logarithmic correction with a small exponent predicted at the BKT transition.…”