Clifford circuits Augmented Matrix Product States for fermion systems

TL;DR

This paper extends Clifford circuits Augmented Matrix Product States (CAMPS) to fermion systems using Jordan-Wigner transformation, demonstrating improved accuracy over traditional MPS in simulating strongly interacting many-body fermion models.

Contribution

The work generalizes CAMPS to fermion systems via Jordan-Wigner transformation, enhancing simulation accuracy for strongly correlated fermionic models.

Findings

Fermionic CAMPS outperforms MPS in accuracy, especially with strong interactions.

Significant improvement in simulating spinless t-V and Hubbard models.

Potential to resolve long-standing issues in many-body fermion system simulations.

Abstract

Clifford circuits Augmented Matrix Product States (CAMPS) was recently proposed to leverage the advantages of both Clifford circuits and Matrix Product States (MPS). Clifford circuits can support large entanglement and can be efficiently simulated classically according to the Gottesman-Knill theorem. So in CAMPS, MPS needs only to handle the so-called Non-stabilizerness Entanglement Entropy which significantly improves the simulation accuracy for a given bond dimension. In this work, we generalize CAMPS to study the Fermion system by taking advantage of the Jordan-Wigner transformation which can map the studied Fermion system to a spin system. We benchmark the method on both the spinless $t-V$ model and the spinful Hubbard model. Our test results show significant improvement of the accuracy of CAMPS over MPS, especially when the interactions are strong. Fermionic CAMPS provides a useful tool for the accurate study of many-body fermion systems in the future and has the potential to help resolve long-standing issues.