Determining system Hamiltonian from eigenstate measurements without correlation functions

Abstract

Local Hamiltonians arise naturally in physical systems. Despite their seemingly 'simple' local structures, exotic features such as non-local correlations and topological orders exhibit in eigenstates of these systems. Previous studies for recovering local Hamiltonians from measurements on an eigenstate require information of nonlocal correlation functions. In this work, we argue that local measurements on is enough to recover the Hamiltonian in most of the cases. Specially, we develop an algorithm to demonstrate the observation. Our algorithm is tested numerically for randomly generated local Hamiltonians of different system sizes and returns promising reconstructions with desired accuracy. Additionally, for random generated Hamiltonians (not necessarily local), our algorithm also provides precise estimations.