Non-Local Order Parameters as a Probe for Phase Transitions in the Extended Fermi-Hubbard Model

TL;DR

This paper demonstrates that non-local order parameters effectively detect phase transitions in the one-dimensional Extended Fermi-Hubbard model, including in conducting and superconducting phases, offering a powerful tool for analyzing complex quantum phases.

Contribution

It introduces non-local operators as reliable probes for phase transitions in the Extended Fermi-Hubbard model, capturing both the nature and location of transitions, including in conducting and superconducting phases.

Findings

Non-local operators detect all phase transitions in the 1D Extended Fermi-Hubbard model.

Asymptotic averages of these operators are finite only in gapped phases.

They serve as effective order parameters for superconducting and paired superfluid phases.

Abstract

The Extended Fermi-Hubbard model is a rather studied Hamiltonian due to both its many applications and a rich phase diagram. Here we prove that all the phase transitions encoded in its one dimensional version are detectable via non-local operators related to charge and spin fluctuations. The main advantage in using them is that, in contrast to usual local operators, their asymptotic average value is finite only in the appropriate gapped phases. This makes them powerful and accurate probes to detect quantum phase transitions. Our results indeed confirm that they are able to properly capture both the nature and the location of the transitions. Relevantly, this happens also for conducting phases with a spin gap, thus providing an order parameter for the identification of superconducting and paired superfluid phases