Properties of gapless systems represented by tensor network ansatz

Wei-Lin Tu^1*

¹Faculty of Science and Technology, Keio University, Yokohama, Japan

* Presenter:Wei-Lin Tu, email:weilintu@keio.jp

In simulating the modern quantum many-body systems many physicists have paid lots of attention to the application of tensor network (TN) ansatz, which is known to be very accurate for gapped systems due to the obedience of area law. However, gapless states, which are known for hosting abundant physics and phenomena, can hardly be as well dealt by TN with finite bond dimension (D). Still, some remnant effects for the ground state can be witnessed by using the TN ansatz. In the first part of my presentation I will talk about our recent results studying the Heisenberg ferromagnet with cubic anisotropy [1]. While a more accurate phase diagram is provided, the emergent phenomenon on the critical phase boundary can also be captured with a finite-D simulation from the infinite projected entangled-pair state. Next, I will show that by using the generating function approach for tensor network diagrammatic summation, previously proposed in the context of matrix product states [2], the effective excited state ansatz can be efficiently constructed for evaluating some further properties in two dimensions [3]. Our benchmark results for the spin-1/2 transverse field Ising model and Heisenberg model on the square lattice provide a desirable accuracy, showing good agreement with known results. We envision that the further application of our methodology can be used to gain more understanding for the peculiar states, such as the gapless spin liquid phase.

References:
[1] Wei-Lin Tu, Xinliang Lyu, S. R. Ghazanfari, Huan-Kuang Wu, Hyun-Yong Lee, and Naoki Kawashima, Phys. Rev. B 107, 224406 (2023).
[2] Wei-Lin Tu, Huan-Kuang Wu, Norbert Schuch, Naoki Kawashima, and Ji-Yao Chen, Phys. Rev. B 103, 205155 (2021).
[3] Wei-Lin Tu, Laurens Vanderstraeten, Norbert Schuch, Hyun-Yong Lee, Naoki Kawashima, and Ji-Yao Chen, arXiv:2307.08083 (2023).

Keywords: Magnetic materials, Magnetocrystalline anisotropy, Quantum phase transition, Tensor network ansatz, Projected entangled-pair state