# Full Counting Statistics for Interacting Fermions with Determinantal Quantum Monte Carlo Simulations

## TL;DR

This paper introduces a method to compute the full probability distribution of quadratic observables in the Fermi-Hubbard model using determinantal quantum Monte Carlo, aiding the analysis of cold atom experiments and magnetic properties.

## Contribution

The paper develops a novel approach for calculating full counting statistics in interacting fermion systems within the determinantal quantum Monte Carlo framework.

## Key findings

- Full counting statistics reveal information on preformed pairs.
- Excellent agreement with experimental measurements of staggered magnetization.
- Current experiments can distinguish between Hubbard and Heisenberg models.

## Abstract

We present a method for computing the full probability distribution function of quadratic observables for the Fermi-Hubbard model within the framework of determinantal quantum Monte Carlo. Especially, in cold atoms experiments with single site resolution, such full counting statistics can be obtained from repeated projective measurements. We demonstrate, that the full counting statistics can provide important information on the size of preformed pairs. Furthermore, we compute the full counting statistics of the staggered magnetization in the repulsive Hubbard model at half filling and find excellent agreement with recent experimental results. We show that current experiments are capable of probing the difference between the Hubbard model and the limiting Heisenberg model.