Generating Function for Projected Entangled-Pair States
Wei-Lin Tu, Laurens Vanderstraeten, Norbert Schuch, Hyun‐Yong Lee, Naoki Kawashima, Ji-Yao Chen
Abstract
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-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mn>1</a:mn><a:mo>/</a:mo><a:mn>2</a:mn></a:math> 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-<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><d:mn>1</d:mn><d:mo>/</d:mo><d:mn>2</d:mn><d:mspace width="0.2em"/><d:msub><d:mi>J</d:mi><d:mn>1</d:mn></d:msub></d:math>-<h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><h:msub><h:mi>J</h:mi><h:mn>2</h:mn></h:msub></h:math> 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. Published by the American Physical Society 2024