Generating Function for Projected Entangled-Pair States

• Published in: PRX quantum Vol. 5; no. 1; p. 010335
• Main Authors: Tu, Wei-Lin, Vanderstraeten, Laurens, Schuch, Norbert, Lee, Hyun-Yong, Kawashima, Naoki, Chen, Ji-Yao
• Format: Journal Article
• Language: English
• Published: American Physical Society 01.03.2024
• ISSN: 2691-3399; 2691-3399
• DOI: 10.1103/PRXQuantum.5.010335

Diagrammatic summation is a common bottleneck in modern applications of projected entangled-pair states, especially in computing low-energy excitations of a two-dimensional quantum many-body system. To solve this problem, here we extend the generating-function approach for tensor-network diagrammatic summation, a scheme previously proposed in the context of matrix product states. Taking the form of a one-particle excitation, we show that the excited state can be computed efficiently in the generating-function formalism, which can further be used in evaluating the dynamical structure factor of the system. 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 then study the spin- 1 / 2 J 1 - J 2 model on the same lattice and investigate the dynamical properties of the putative gapless spin liquid phase. We conclude with a discussion on generalizations to multiparticle excitations.