Matrix product ansatz for Fermi fields in one dimension

TL;DR

This paper develops a continuous matrix product state approach for one-dimensional two-component fermions, effectively capturing ground state properties and correlations in an interacting spin-1/2 Fermi gas.

Contribution

It introduces a variational matrix construction that respects translational symmetry and regularity conditions, improving the modeling of fermionic systems.

Findings

Accurately predicts ground state magnetic properties

Captures phase-oscillating pair correlations

Validates approach on interacting spin-1/2 system

Abstract

We present an implementation of a continuous matrix product state for two-component fermions in one-dimension. We propose a construction of variational matrices with an efficient parameterization that respects the translational symmetry of the problem (without being overly constraining) and readily meets the regularity conditions that arise from removing the ultraviolet divergences in the kinetic energy. We test the validity of our approach on an interacting spin-1/2 system and observe that the ansatz correctly predicts the ground state magnetic properties for the attractive spin-1/2 Fermi gas, including the phase-oscillating pair correlation function in the partially polarized regime.