Tensor network ansatz for the quantum many-body models: Case studies and advanced algorithms

Wei-Lin Tu^1*

¹Division of Display and Semiconductor Physics, Korea University, Sejong, Korea

* Presenter:Wei-Lin Tu, email:weilintu@korea.ac.kr

In our nature, the macroscopic behavior of the materials can often be understood by their microscopic properties such as various symmetries, giving rise to different many-body models. However, to analytically solve these models in the thermodynamic limit is in most of the cases an unachievable task. On the other hand, by exploiting the capability of modern computational devices an effective “ansatz” can be constructed who serves as a good variational approximation for the target model. In this talk, I am going to introduce how theorists can adopt the tensor network algorithm as the tool in grasping the ground state or excited state properties for a quantum many-body system. Utilizing the infinite projected entangled-pair state (iPEPS) we get to study the physics of various systems in two dimensions (2D), such as a frustrated or dipolar artificial magnet in an optical lattice [1,2], and the real-world quantum magnetism [3,4]. A recent development combining the merits of two distinct optimization methods, the imaginary-time evolution and variational optimization, provides a better insight into the model of interest [5]. Besides the ground state, by summing up various tensor graphs an effective one-particle excited state ansatz can also be probed and computationally simplified using the mathematical generating function with back propagation. Besides our early success for matrix product state in one dimension [6], I will also provide some preliminary results under development in 2D. I hope that my brief introduction and examples provided here can arouse a wider interest in adopting this algorithm in various aspects.

References
[1] Wei-Lin Tu, Huan-Kuang Wu, and Takafumi Suzuki, Journal of Physics: Condensed Matter 32, 455401 (2020).
[2] Huan-Kuang Wu and Wei-Lin Tu, Physical Review A 102, 053306 (2020).
[3] Wei-Lin Tu, Eun-Gook Moon, Kwan-Woo Lee, Warren E. Pickett, and Hyun-Yong Lee, Communications Physics 5, 130 (2022).
[4] Wei-Lin Tu, Xinliang Lyu, S. R. Ghazanfari, Huan-Kuang Wu, Hyun-Yong Lee, and Naoki Kawashima, arXiv:2204.01197 (2022).
[5] Yu-Hsueh Chen, Ke Hsu, Wei-Lin Tu, Hyun-Yong Lee, and Ying-Jer Kao, arXiv:2207.01819 (2022) (Accepted by Physical Review Research).
[6] Wei-Lin Tu, Huan-Kuang Wu, Norbert Schuch, Naoki Kawashima, and Ji-Yao Chen, Physical Review B 103, 205155 (2021).

Keywords: Quantum Many-body Systems, Tensor Network, Phase Diagram, Phase Transition, Quantum Magnetism