Fermionic tensor network contraction for arbitrary geometries

TL;DR

This paper presents a flexible fermionic tensor network contraction method applicable to arbitrary lattice geometries, with implementations in the quimb library, enabling advanced simulations of complex quantum many-body systems.

Contribution

It introduces a comprehensive implementation of fermionic tensor network contraction for arbitrary geometries, including two formal conventions and optimized strategies, demonstrated on complex lattice models.

Findings

Successful benchmarking on 3D diamond lattice Hubbard models

Effective approximate contraction strategies for complex geometries

Implementation details for fermionic tensor networks in quimb

Abstract

We describe our implementation of fermionic tensor network contraction on arbitrary lattices within both a globally ordered and locally ordered formalism. We provide a pedagogical description of these two conventions as implemented for the quimb library. Using hyperoptimized approximate contraction strategies, we present benchmark fermionic projected entangled pair states simulations of finite Hubbard models defined on the three-dimensional diamond lattice and random regular graphs.