Lanczos steps to improve variational wave functions

TL;DR

This paper demonstrates that applying Lanczos steps to Gutzwiller-projected fermionic states enhances the accuracy of variational wave functions for frustrated Heisenberg models, enabling reliable energy estimations on large clusters.

Contribution

It introduces a method of using Lanczos steps to improve variational wave functions for frustrated quantum spin models, extending computational capabilities.

Findings

Improved variational energies with Lanczos steps

Reliable energy and variance estimates for large clusters

Enhanced accuracy for frustrated Heisenberg models

Abstract

Gutzwiller-projected fermionic states can be efficiently implemented within quantum Monte Carlo calculations to define extremely accurate variational wave functions for Heisenberg models on frustrated two-dimensional lattices, not only for the ground state but also for low-energy excitations. The application of few Lanczos steps on top of these states further improves their accuracy, allowing calculations on large clusters. In addition, by computing both the energy and its variance, it is possible to obtain reliable estimations of exact results. Here, we report the cases of the frustrated Heisenberg models on square and Kagome lattices.