Tensor Networks Can Resolve Fermi Surfaces

TL;DR

This paper shows that tensor network states, specifically PEPS, can efficiently represent the ground states of critical fermionic systems with Fermi surfaces, achieving arbitrary precision by increasing bond dimension.

Contribution

It demonstrates that PEPS can accurately model fermionic systems with Fermi surfaces, with controlled precision scaling, addressing challenges of nonanalyticities and topology.

Findings

Energy precision improves as a power law with bond dimension.

Finite size results extrapolate to the thermodynamic limit.

Boundary conditions and system sizes are crucial for avoiding nonanalyticities.

Abstract

We demonstrate that projected entangled-pair states (PEPS) are able to represent ground states of critical, fermionic systems exhibiting both 1d and 0d Fermi surfaces on a 2D lattice with an efficient scaling of the bond dimension. Extrapolating finite size results for the Gaussian restriction of fermionic projected entangled-pair states to the thermodynamic limit, the energy precision as a function of the bond dimension is found to improve as a power law, illustrating that an arbitrary precision can be obtained by increasing the bond dimension in a controlled manner. In this process, boundary conditions and system sizes have to be chosen carefully so that nonanalyticities of the Ansatz, rooted in its nontrivial topology, are avoided.