前沿量子科技研究中心量子資訊專題演講
Real Space Renormalization Group via Tenor Network
In this talk, I will discuss how to reincarnate the concept of real space renormalization group in modern tensor network language.
As an example, I perform tensor network based finite-size scaling analysis for the two-dimensional classical Ising model.
I consider an infinite strip and use the higher-order tensor renormalization group method to renormalize the transfer matrix,
from which the correlation length, spontaneous magnetization, and latent heat can be evaluated.
I show that, by applying standard finite-size scaling techniques, critical temperature Tc and critical exponents nu, beta, alpha can be accurately determined.
Furthermore, the conformal data can be accurately extracted.
In contrast to the early real space renormalization group method, here the results can be systematically improved.
In addition, I will discuss the nature crossover length scale included by the finite bond dimension.
Finally, I will discuss the quantum-classical correspondence and how to define entanglement for the classical models and the link to the conformal field theory.
As an example, I perform tensor network based finite-size scaling analysis for the two-dimensional classical Ising model.
I consider an infinite strip and use the higher-order tensor renormalization group method to renormalize the transfer matrix,
from which the correlation length, spontaneous magnetization, and latent heat can be evaluated.
I show that, by applying standard finite-size scaling techniques, critical temperature Tc and critical exponents nu, beta, alpha can be accurately determined.
Furthermore, the conformal data can be accurately extracted.
In contrast to the early real space renormalization group method, here the results can be systematically improved.
In addition, I will discuss the nature crossover length scale included by the finite bond dimension.
Finally, I will discuss the quantum-classical correspondence and how to define entanglement for the classical models and the link to the conformal field theory.
