Lanczos Boosted Numerical Linked-Cluster Expansion for Quantum Lattice Models

TL;DR

This paper introduces a Lanczos-based partial diagonalization technique to enhance numerical linked-cluster expansions for quantum lattice models, significantly improving computational efficiency for large clusters.

Contribution

It presents a novel approach combining Lanczos partial diagonalization with linked-cluster expansions, reducing computational costs while maintaining accuracy.

Findings

Efficient calculation of thermodynamic properties for quantum lattice models.

Significant reduction in time and memory usage with Lanczos method.

Applicable to frustrated Heisenberg models on checkerboard lattices.

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 a test case, we consider a frustrated Heisenberg model on the checkerboard lattice and find that our approach can lead to much more efficient calculations in a parallel environment.