Grassmann tensor networks

TL;DR

This paper introduces Grassmann tensor network methods for strongly correlated fermionic systems, providing foundational explanations and validating their effectiveness in models from physics.

Contribution

It offers a comprehensive, self-contained introduction to Grassmann tensor networks and demonstrates their practical application in physics models.

Findings

Validated Grassmann tensor network methods in models from particle physics and condensed matter physics.

Provided detailed algorithms for Grassmann tensor operations.

Highlighted the underexploited potential of Grassmann tensor networks in simulations.

Abstract

Developing non-perturbative methods to reveal exotic properties of strongly correlated fermionic systems remains one of the most essential tasks of theoretical physics. Tensor network methods with Grassmann algebra offer powerful numerical tools for fermionic many-body systems in the coherent-state path-integral representation. Despite their vast potential for both condensed-matter and particle-physics communities, Grassmann tensor network methods are somewhat underexploited in practical simulations. In this work, we provide a detailed, self-contained introduction to Grassmann tensor network methods, from the basics of the Grassmann tensor operations to the Grassmannization of typical tensor network algorithms. Furthermore, the resulting Grassmann tensor network methods are validated in several interesting models in both particle physics and condensed matter physics.