Green Function Monte Carlo with Stochastic Reconfiguration

TL;DR

This paper introduces a stochastic reconfiguration method to stabilize the sign problem in Green Function Monte Carlo simulations for lattice Hamiltonians, enabling more reliable studies of frustrated quantum spin systems.

Contribution

It proposes a novel iterative stochastic reconfiguration scheme that stabilizes Green Function Monte Carlo simulations, allowing for controlled bias reduction in sign problem scenarios.

Findings

Evidence of a finite spin gap for J2/J1 >~ 0.4 in the thermodynamic limit

Method successfully applied to the frustrated J1-J2 Heisenberg model

Stable simulations with constant sign achieved

Abstract

A new method for the stabilization of the sign problem in the Green Function Monte Carlo technique is proposed. The method is devised for real lattice Hamiltonians and is based on an iterative ''stochastic reconfiguration'' scheme which introduces some bias but allows a stable simulation with constant sign. The systematic reduction of this bias is in principle possible. The method is applied to the frustrated J1-J2 Heisenberg model, and tested against exact diagonalization data. Evidence of a finite spin gap for J2/J1 >~ 0.4 is found in the thermodynamic limit.