Quantum circuits reproduce the experimental two-dimensional many-body localization transition point

While many studies point towards the existence of many-body localization (MBL) in one dimension, the fate of higher-dimensional strongly disordered systems is a topic of current debate. The latest experiments as well as several recent numerical studies indicate that such systems behave many-body localized—at least on practically relevant timescales. However, thus far, theoretical approaches have been unable to quantitatively reproduce experimentally measured MBL features—an important requirement to demonstrate their validity. In this Letter, we use fermionic quantum circuits as a variational method to approximate the full set of eigenstates of two-dimensional MBL systems realized in fermionic optical lattice experiments. Using entanglement-based features, we obtain a phase transition point in excellent agreement with the experimentally measured value. Moreover, we calculate the filling-fraction-dependent MBL phase diagram. We argue that our approach best captures the underlying charge-density-wave experiments and compute the mean localization lengths, which can be compared to future experiments.