Lanczos-boosted numerical linked-cluster expansion for quantum lattice models

Abstract

Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the limiting factor for these calculations. Here we show that a partial diagonalization of the largest clusters in the expansion using the Lanczos algorithm can be as useful as full diagonalization for the method while mitigating some of the time and memory issues. As test cases, we consider the frustrated Heisenberg model on the checkerboard lattice and the Fermi-Hubbard model on the square lattice. We find that our approach can surpass state of the art in performance in a parallel environment.