Accurate simulation for finite projected entangled pair states in two dimensions

Abstract

Projected entangled pair states (PEPS) methods provide promising ways to simulate quantum many-body lattice models in two and higher dimensions. Unfortunately, the expensive computational cost scaling of PEPS has been a stumbling block for accurate simulations in practical applications. In this paper, we develop an optimized finite PEPS algorithm based on the scheme of variational Monte Carlo sampling. Our algorithm makes it possible to simulate quantum spin systems as large as \(32 \times 32\) sites accurately. Benchmark results on the square-lattice antiferromagnetic Heisenberg model including ground state energy and spin correlations excellently agree with Quantum Monte Carlo results. For highly frustrated spin models, our results are also in excellent agreement with those obtained from density matrix renormalization group method. Thus, we establish an accurate finite PEPS algorithm in two dimensions, and it potentially opens a new door towards resolving many challenging strongly correlated quantum many-body problems.