Tensor Network Calculation of the Logarithmic Correction Exponent in the <i>XY</i> Model

We study the logarithmic correction to scaling of first Lee-Yang (LY) zero in classical $XY$ model on square lattices by using tensor renormalization group methods. In comparing higher-order (HOTRG) and loop-optimized network (LoopTNR), we find that entanglement filtering LoopTNR is crucial gaining high accuracy for characterization correction, while HOTRG still proposes approximate bounds location associated with two different bond-merging algorithms singular value decomposition oblique projectors. Using data computed up system size $L=1024$ $L \times L$ lattices, estimate exponent $r = -0.0643(9)$ from extrapolation finite-size effective exponent, which comparable prediction -1/16$.