Fermionic implementation of projected entangled pair states algorithm

2010/03/31 by Iztok Pižorn, Iztok Pizorn, Frank Verstraete · 1 citation
Mathematics · Physics and Astronomy · #Algorithm #Bilinear interpolation #Ising model #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Square lattice #String (physics) #Tensor decomposition and applications #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevb.81.245110

published as Phys. Rev. B 81 245110 (2010) · As published in Phys. Rev. B

openalex publication_date 2010/06/09 · arxiv created 2010/06/14 · arxiv updated 2010/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present and implement an efficient variational method to simulate two-dimensional finite-size fermionic quantum systems by fermionic projected entangled pair states. The approach differs from the original one due to the fact that there is no need for an extra string bond for contracting the tensor network. The method is tested on a bilinear fermionic model on a square lattice for sizes up to ten by ten where good relative accuracy is achieved. Qualitatively good results are also obtained for an interacting fermionic system.

Citations

• Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative Systems
• Colloquium: Area laws for the entanglement entropy
• Density Matrix Renormalization Group and Periodic Boundary Conditions: A Quantum Information Perspective
• Efficient Simulation of One-Dimensional Quantum Many-Body Systems
• Fermionic projected entangled pair states
• Matrix product states represent ground states faithfully
• Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems

Cited by

• Generalization of the exponential basis for tensor network representations of long-range interactions in two and three dimensions