Effective hamiltonian approach and the lattice fixed node approximation

TL;DR

This paper introduces a numerical scheme to approximate Hamiltonians with effective ones, improving the lattice fixed node method and enabling accurate Quantum Monte Carlo solutions that are less sensitive to the guiding function.

Contribution

It presents a new approach to define effective Hamiltonians using constraints from short-range properties, enhancing the fixed node approximation and addressing sensitivity issues in variational Monte Carlo.

Findings

Effective Hamiltonian can be solved exactly by Quantum Monte Carlo.

Long distance, low energy properties are largely independent of the guiding function.

Improved variational energy estimates compared to standard methods.

Abstract

We define a numerical scheme that allows to approximate a given Hamiltonian by an effective one, by requiring several constraints determined by exact properties of generic ''short range'' Hamiltonians. In this way the standard lattice fixed node is also improved as far as the variational energy is concerned. The effective Hamiltonian is defined in terms of a guiding function $\psi_G$ and can be solved exactly by Quantum Monte Carlo methods. We argue that, for reasonable $\psi_G$ and away from phase transitions, the long distance, low energy properties are rather independent on the chosen guiding function, thus allowing to remove the well known problem of standard variational Monte Carlo schemes based only on total energy minimizations, and therefore insensitive to long distance low energy properties.