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).