An Improved Infinite Time-Evolving Block Decimation Algorithm Applied to SU(N) Antiferromagnetic Heisenberg Chains

Abstract

The infinite time-evolving block decimation (iTEBD) algorithm provides an efficient way to search for the ground state of a one-dimensional lattice system with translational invariance at the thermodynamic limit, especially for systems with limited entanglement. However, for systems with large on-site physical degrees of freedom, especially for the antiferromagnetic Heisenberg (AFH) chain with SU(N) symmetries, the decompositions in the iTEBD calculation become extremely heavy, even for a small virtual bond dimension. In this work, we consider a revised low-rank approximation by Monte Carlo sampling in the decomposition process. Our results show that compared to the original iTEBD algorithm, the proposed algorithm achieves faster convergence with comparable accuracy. Based on this algorithm, we calculate the ground state energy of the SU(3) AFH model with representation \(\varvec{10}\) and find evidence that the ground state belongs to a trivial symmetry-protected topological phase.