Neural Polaron: Learning Quasiparticle Operators in Quantum Many-Body Systems

Abstract

Understanding dynamical properties of quantum many-body systems remains a central challenge because excitations generally require information beyond a ground-state wave function. Here we introduce a neural polaron ansatz that represents quasiparticle excitations by neural many-body operators acting on a correlated ground state. Instead of learning an independent excited-state wave function, the method parameterizes a local dressing operator through a compact neural head defined on the feature map of a pretrained ground-state network. This operator-based construction builds in translation symmetry, momentum resolution, and quasiparticle locality, while separating ground-state correlations from excitation-specific dressing. We benchmark the method on the square-lattice $J_1$-$J_2$ Heisenberg model, where it accurately reproduces magnon dispersions and spectral weights over a broad range of frustration. In particular, it captures nontrivial many-body features including the $(π,0)$ anomaly and its progressive softening with increasing $J_2/J_1$. These results establish neural operators as a physically transparent route for extending neural quantum states from ground-state properties to dynamical response.