Numerical renormalization group integrated Hamiltonian truncation: Toward generic deformation of integrable lattice models

We present a hybrid lattice Hamiltonian truncation method that integrates the numerical renormalization group (NRG) with a truncated lattice integrable spectrum. The technique is tailored for generic deformations of integrable lattice models, where the NRG enables a controlled incorporation of high-energy states. The method extends the basis set more effectively and efficiently than brute-force truncation, meanwhile significantly reducing errors. We show its capability on two paradigmatic models: an Ising chain in a magnetic field and a quantum Ising ladder. The resulting dynamical structure factors accurately capture the essential low-energy physics, including the $E_8$ and $\mathcal{D}_8^{(1)}$ excitations of the former and later models, respectively, demonstrating the approach's computational efficiency and high performance.