Stacked tree construction for free-fermion projected entangled pair states

TL;DR

This paper introduces a divide-and-conquer method to directly construct PEPS representations for free-fermion states using local tree tensor networks and stacking, improving efficiency in higher-dimensional tensor network states.

Contribution

It presents a novel approach to directly build PEPS for free-fermion states by combining local tree tensor networks through stacking, bypassing traditional variational methods.

Findings

Successfully constructed PEPS for 1D and 2D free-fermion states.

Demonstrated application to an obstructed atomic insulator on a square lattice.

Achieved more efficient tensor network representations through local tensor compression.

Abstract

The tensor network representation of a state in higher dimensions, say a projected entangled-pair state (PEPS), is typically obtained indirectly through variational optimization or imaginary-time Hamiltonian evolution. Here, we propose a divide-and-conquer approach to directly construct a PEPS representation for free-fermion states admitting descriptions in terms of filling exponentially localized Wannier functions. Our approach relies on first obtaining a tree tensor network description of the state in local subregions. Next, a stacking procedure is used to combine the local trees into a PEPS. Lastly, the local tensors are compressed to obtain a more efficient description. We demonstrate our construction for states in one and two dimensions, including the ground state of an obstructed atomic insulator on the square lattice.