Constructive Fermionic Matrix Product States for Projected Fermi Sea

TL;DR

This paper introduces a constructive tensor-network method to compute physical observables in projected Fermi sea states, enabling analysis of gapless electronic phases with local correlations.

Contribution

It develops a novel tensor-network approach for calculating physical quantities in one-dimensional projected Fermi sea states, validated against analytical results and applied to correlated fermion systems.

Findings

Accurately computes fermion two-point and density-density correlation functions.

Benchmarks against exact analytical results for Gutzwiller-projected spin-1/2 electrons.

Reveals correlation-tuned charge density wave vectors in systems with multiple Fermi points.

Abstract

Projected wave functions offer a means for incorporating local correlation effects in gapless electronic phases of matter like metals. Although such wave functions can be readily specified formally, it is challenging to compute their associated physical observables. Tensor network approaches offer a modern numerical method for this task. In this work, we develop and demonstrate a constructive tensor-network approach for obtaining physical quantities, like fermion two-point functions and density-density correlation functions, for one-dimensional projected Fermi sea states. We benchmark our method against exact analytical results for spin-1/2 electrons subjected to the Gutzwiller projection, and then present results on spinless fermions with nearest-neighbor repulsion. For a state with two pairs of Fermi points, we reveal a correlation-tuning of the characteristic wave vector of the charge density modulation in the system.