Algorithms for variational Monte Carlo calculations of fermion projected entangled pair states in the swap gates formulation and the detailed balance of tensor network sequential sampling

2025/06/25 by Yantao Wu, Wu, Yantao, Zhehao Dai +1 · 3 citations
Physics and Astronomy · #FOS: Physical sciences #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.str-el

paper · pdf · doi:10.48550/arxiv.2506.20106

hubbard figure

arxiv created 2026/08/03 · arxiv updated 2026/08/04

Abstract

In recent years, the variational Monte Carlo (VMC) calculations of projected entangled pair states (PEPS) has emerged as a competitive method for computing the ground states of many-body quantum systems. This method is particularly important for fermion systems where sign problems are abundant. We derive and explain the algorithms for the VMC calculations of fermion PEPS in the swap gates formulation. As a separate key result, we prove the detailed balance of sequential sampling of tensor networks.

Citations

• Accurate Simulation of the Hubbard Model with Finite Fermionic Projected Entangled Pair States
• Fermionic Isometric Tensor Network States in Two Dimensions
• Grassmann tensor network states and its renormalization for strongly correlated fermionic and bosonic states
• Graded Projected Entangled-Pair State Representations and An Algorithm for Translationally Invariant Strongly Correlated Electronic Systems on Infinite-Size Lattices in Two Spatial Dimensions
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Sign problem in the numerical simulation of many-electron systems

Cited by

• Holographic Representation of One-Dimensional Many-Body Quantum States via Isometric Tensor Networks
• Real-Time Dynamics in Two Dimensions with Tensor Network States via Time-Dependent Variational Monte Carlo
• Functional Neural Wavefunction Optimization

Related

• Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach
• Algorithmic aspects of gauged Gaussian fermionic projected entangled pair states
• Accurate Simulation of the Hubbard Model with Finite Fermionic Projected Entangled Pair States
• Real-Time Dynamics in Two Dimensions with Tensor Network States via Time-Dependent Variational Monte Carlo
• A unified theory of variational and quantum Monte Carlo methods and beyond