Explore Scale Invariant Hamiltonian in Efimov Physics Using Quantized Tensor Train Approach

Che-Chia Hsu^1*, Tao-Lin Tan¹, Chia-Min Chung², Yi-Ping Huang¹

¹Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
²Department of Physics, National Sun Yat-sen University, Kaohsiung, Taiwan

* Presenter:Che-Chia Hsu, email:charles123756@gapp.nthu.edu.tw

Matrix product state (MPS) is a 1D structure in the tensor network (TN) that can store the 1D quantum state. MPS is impressive because it can reduce memory significantly if the quantum state is low-entangled. Therefore, MPS is a powerful data compression structure and can be applied to other kinds of data if the data is equivalent to the low-entangled state. A recent study has shown the discrete smooth functions exhibit low-entangled states and can be represented by MPS in low memory. As a result, many memory-related numerical challenges may be overcome, and physicists have successfully applied MPS to some fields, such as complex dynamics. This study endeavors to apply MPS to Efimov physics, which is characterized by scaling invariance. Two new distinct approaches for generating the potential with the inverse square of the distance into MPS using the quantized tensor train (QTT) approach have been used in this study, successfully reproducing discrete scaling invariance and energy ratio invariance features with high precision and less memory using density matrix renormalization group (DMRG).

Keywords: Tensor Network, Efimov Physics, Quantized Tensor Train