# Measuring the topological phase transition via the single-particle density matrix

## TL;DR

This paper presents a method to detect topological phase transitions in interacting fermionic systems using the single-particle density matrix, with a practical tomography scheme for cold atom experiments.

## Contribution

It introduces a way to identify topological phases via the single-particle density matrix and proposes an experimental tomography scheme for cold atom systems.

## Key findings

- Berry curvature and Chern number can be extracted from the density matrix.
- Topological phase transition points are identifiable through this method.
- A feasible tomography scheme for cold atom experiments is designed.

## Abstract

We discuss the topological phase transition of the spin-$\frac{1}{2}$ fermionic Haldane model with repulsive on-site interaction. We show that the Berry curvature of the topological Hamiltonian, the first Chern number, and the topological phase transition point can be extracted from the single-particle density matrix for this interacting system. Furthermore, we design a tomography scheme for the single-particle density matrix of interacting fermionic two-band models in experimental realizations with cold atoms in optical lattices.