J1-J2 Fractal by Multi-Recursion HOTRG

Jozef Genzor^1*, Ying-Jer Kao¹

¹Department of Physics, National Taiwan University, Taipei, Taiwan

* Presenter:Jozef Genzor, email:jozef.genzor@gmail.com

We develop a novel technique to study phase transition phenomena on self-similar lattices constructed on a square-lattice frame with two different coupling strengths. By introducing two types of couplings, it is possible to continuously transform a regular square lattice into a fractal lattice by adjusting some couplings determined by the underlying fractal pattern. In extreme cases, a pure fractal lattice is obtained when specified bonds are cut by setting one of the couplings to be equal to zero, and regular square lattice is recovered when both couplings are equal to one. We are able to perform measurements by means of impurity tensors in any regime between and including a pure fractal lattice and regular square lattice. Instead of having one type of local tensor and one extension relation as in the Higher-Order Tensor Renormalization Group (HOTRG) algorithm, we introduce several types of local tensors with each being extended by a different recursive relation. The computational cost scales with the bond dimension in the same way as in the 2D HOTRG with a constant-factor overhead.

Keywords: Phase transitions, Ising model, HOTRG, Fractals