Signatures of correlated magnetic phases in the local two-particle density matrix

TL;DR

This paper demonstrates how measurements of the two-spin density matrix and its statistics can identify various correlated magnetic phases in the Fermi-Hubbard model, aiding experimental detection of complex quantum states.

Contribution

It introduces a method to use local two-particle density matrix measurements to distinguish magnetic phases, including long-range ordered and topologically ordered states.

Findings

Predicts doping and temperature dependence of local correlators.

Identifies signatures of different magnetic phases in the Hubbard model.

Provides a framework for experimental detection of quantum magnetic states.

Abstract

Experiments with quantum gas microscopes have started to explore the antiferromagnetic phase of the two-dimensional Fermi-Hubbard model and effects of doping with holes away from half filling. In this work we show how direct measurements of the system averaged two-spin density matrix and its full counting statistics can be used to identify different correlated magnetic phases with or without long-range order. We discuss examples of phases which are potentially realized in the Hubbard model close to half filling, including antiferrromagnetically ordered insulators and metals, as well as insulating spin-liquids and metals with topological order. For these candidate states we predict the doping- and temperature dependence of local correlators, which can be directly measured in current experiments.