Construction of Hamiltonians by supervised learning of energy spectra

Handling the large number of degrees of freedom with proper approximations, namely the construction of the effective Hamiltonian is at the heart of the (condensed matter) physics. Here we propose a simple scheme of constructing Hamiltonians from a given energy spectrum [1]. The sparse nature of the physical Hamiltonians allows us to formulate this as a solvable supervised learning problem. Taking a simple model of correlated electron systems, we demonstrate the data-driven construction of its low-energy effective model. We present potential applications for the construction of entanglement Hamiltonians and materials discovery through the construction of parent Hamiltonians from effective models of topological matters. [1]H.Fujita et.al., Phys. Rev. B 97, 075114 (2018).