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

arXiv:2205.02773Journal of the Physical Society of JapanJul 27, 20229 citations

Dynamics of the one-dimensional isotropic XY-model

L.L. Gonçalves, H.B. Cruz

Journal of Magnetism and Magnetic MaterialsJan 1, 198011 citations

Doubling of entanglement spectrum in tensor renormalization group

Hiroshi Ueda, Kouichi Okunishi, Tomotoshi Nishino

We investigate the entanglement spectrum in HOTRG---tensor renormalization group (RG) method combined with the higher order singular value decomposition---for two-dimensional (2D) classical vertex models. In the off-critical region, it is explained that the entanglement spectrum associated with the RG transformation is described by ``doubling'' of the spectrum of a corner transfer matrix. We then demonstrate that the doubling actually occurs for the square-lattice Ising model by HOTRG calculations up to $D=64$ , where $D$ is the cutoff dimension of tensors. At the critical point, we also find that a nontrivial $D$ scaling behavior appears in the entanglement entropy. We mention about the HOTRG for the 1D quantum system as well.We investigate the entanglement spectrum in HOTRG---tensor renormalization group (RG) method combined with the higher order singular value decomposition---for two-dimensional (2D) classical vertex models. In the off-critical region, it is explained that the entanglement spectrum associated with the RG transformation is described by ``doubling'' of the spectrum of a corner transfer matrix. We then demonstrate that the doubling actually occurs for the square-lattice Ising model by HOTRG calculations up to $D=64$, where $D$ is the cutoff dimension of tensors. At the critical point, we also find that a nontrivial $D$ scaling behavior appears in the entanglement entropy. We mention about the HOTRG for the 1D quantum system as well.

arXiv:1306.6829Physical Review BFeb 14, 201433 citations

We study the logarithmic correction to the scaling of the first Lee-Yang (LY) zero in the classical

XY

model on square lattices by using tensor renormalization group methods. In comparing the higher-order tensor renormalization group (HOTRG) and the loop-optimized tensor network renormalization (LoopTNR), we find that the entanglement filtering in LoopTNR is crucial to gaining high accuracy for the characterization of the logarithmic correction, while HOTRG still proposes approximate bounds for the zero location associated with two different bond-merging algorithms of the higher-order singular value decomposition and the oblique projectors. Using the LoopTNR data computed up to the system size of

L=1024

in the

L \times L

lattices, we estimate the logarithmic correction exponent

r = -0.0643(9)

from the extrapolation of the finite-size effective exponent, which is comparable to the renormalization group prediction of

r = -1/16

D=64

, where

D

is the cutoff dimension of tensors. At the critical point, we also find that a nontrivial

D

scaling behavior appears in the entanglement entropy. We mention about the HOTRG for the 1D quantum system as well.