Matrix Product States for Quantum Many-Fermion Systems

TL;DR

This paper introduces a straightforward method for finding ground state energies in quantum many-fermion systems using matrix product states, avoiding expectation value calculations, and effectively handling fermion exchange effects.

Contribution

It presents a novel approach to efficiently compute ground state energies in fermionic systems with tensor networks, improving upon existing methods by simplifying the process.

Findings

Accurately determines ground state energy in spinless fermion systems.

Effectively accounts for fermion exchange effects in tensor network updates.

Provides results consistent with exact solutions in finite systems.

Abstract

We describe a simple method to find the ground state energy without calculating the expectation value of the Hamiltonian in the time-evolving block decimation algorithm with tensor network states. For example, we consider quantum many-fermion systems with matrix product states, which are updated consistently in a way that accounts for fermion exchange effects. This method can be applied to a wide class of fermion systems. We test this method in spinless fermion system where the exact ground state energy is known. We analyze finite size effects to determine the ground state energy in the thermodynamic limit that is compared to the exact value.