Quantum Monte Carlo diagonalization for many-fermion systems

TL;DR

This paper introduces a quantum Monte Carlo diagonalization method for many-fermion systems that avoids the negative sign problem by expanding the ground-state wave function in a basis and optimizing it through diagonalization and genetic algorithms.

Contribution

The paper presents a novel quantum Monte Carlo diagonalization approach that eliminates the negative sign problem and employs genetic algorithms for wave function optimization.

Findings

Accurate ground-state energies for small clusters

Correlation functions consistent with existing data

Method effectively avoids the negative sign problem

Abstract

In this study we present an optimization method based on the quantum Monte Carlo diagonalization for many-fermion systems. Using the Hubbard-Stratonovich transformation, employed to decompose the interactions in terms of auxiliary fields, we expand the true ground-state wave function. The ground-state wave function is written as a linear combination of the basis wave functions. The Hamiltonian is diagonalized to obtain the lowest energy state, using the variational principle within the selected subspace of the basis functions. This method is free from the difficulty known as the negative sign problem. We can optimize a wave function using two procedures. The first procedure is to increase the number of basis functions. The second improves each basis function through the operators, $e^{-\Delta\tau H}$, using the Hubbard-Stratonovich decomposition. We present an algorithm for the Quantum Monte Carlo diagonalization method using a genetic algorithm and the renormalization method. We compute the ground-state energy and correlation functions of small clusters to compare with available data.