Numerical evidence for many-body localization in two and three-dimensions

Typically, quantum systems obey the laws of statistical mechanics and reach thermal equilibrium with their environment. However, many-body localization (MBL), a phenomenon that occurs in the presence of strong disorder and interactions, can give rise to quasi-local conserved quantities known as l-bits that prevent thermalization. While MBL has been shown to exist in 1D, a difficult open question has been to determine to what extent MBL exists in higher spatial dimension. In this talk, we present an algorithm [1] for finding approximate l-bits that we use to probe MBL physics in the disordered Heisenberg model in one, two, and three spatial dimensions and the hard-core Bose-Hubbard model in two dimensions. In all models studied, we find numerical signatures of a thermal-MBL transition and observe agreement with past observations of transitions in the 1D Heisenberg model and 2D hard-core Bose-Hubbard model. We make the first numerical observation of a transition to MBL physics in three dimensions.

[1] E. Chertkov, B. Villalonga, and B. K. Clark, arXiv:2007.02959 (2020).