Optimal local basis truncation of lattice quantum many-body systems

Abstract

We show how to optimally reduce the local Hilbert basis of lattice quantum many-body (QMB) Hamiltonians. The basis truncation exploits the most relevant eigenvalues of the estimated single-site reduced density matrix (RDM). It is accurate and numerically stable across different model phases, even close to quantum phase transitions. We apply this procedure to different models, such as the Sine-Gordon model, the $\varphi^{4}$ theory, and lattice gauge theories, namely Abelian $\mathrm{U}(1)$ and non-Abelian $\mathrm{SU}(2)$, in one and two spatial dimensions. Our results reduce state-of-the-art estimates of computational resources for classical and quantum simulations.