# Quantum state tomography on a plaquette in the 2D Hubbard model

## TL;DR

This paper demonstrates that quantum state tomography on a small subsystem within the 2D Hubbard model can be achieved using determinantal quantum Monte Carlo simulations, providing detailed insights into local quantum states.

## Contribution

It introduces a method to extract complete quantum state information of a small subsystem from Monte Carlo simulations, including both diagonal and off-diagonal elements of the reduced density matrix.

## Key findings

- Successfully computed the reduced density matrix for a plaquette in the Hubbard model.
- Applied symmetry and particle number conservation to analyze eigenvalues.
- Provides benchmark data for quantum gas microscope experiments.

## Abstract

Motivated by recent quantum gas microscope experiments for fermions in optical lattices, we present proof of principle calculations showing that it is possible to obtain the complete information about the quantum state on a small subsystem from equilibrium determinantal quantum Monte Carlo simulations. Both diagonal (in the occupation number basis) and off-diagonal elements of the reduced density matrix are calculated for a square plaquette, which is embedded in a much larger system of the two-dimensional Hubbard model, both at half filling and in the doped case. The diagonalization of the reduced density matrix is done by exploiting the point group symmetry and particle number conservation, which allows to attach symmetry labels to its eigenvalues. Knowledge of the probabilities of plaquette occupation number configurations is useful for meticulous benchmarking of quantum gas microscope experiments. As the quantum state on the plaquette is exact and self-consistently embedded in an exact, correlated bath, the present approach connects to various cluster approximation techniques.