Ground-state properties via machine learning quantum constraints

Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert space has made such studies costly, if not prohibitive, on sufficiently large system sizes. Here, we propose an alternative strategy based upon the expectation values of an ensemble of operators and the elusive yet vital quantum constraints between them, where the search for ground-state properties simply equates to simple, classical constrained minimization. These quantum constraints are generally obtainable via machine learning on a large number of sample quantum many-body states systematically consistent with physical presumptions. We showcase our perspective on 1D fermion chains and spin chains for applicability, effectiveness, and several unique advantages, especially for strongly correlated systems, thermodynamic-limit systems, property designs, etc.Comment: 6 pages, 4 figure