A Quantum Monte Carlo Method at Fixed Energy

TL;DR

This paper introduces a novel Quantum Monte Carlo method that fixes the ground state energy as a parameter, enabling the study of zero temperature quantum systems without referencing transition times.

Contribution

It develops a fixed-energy Quantum Monte Carlo approach that allows direct computation of ground state properties by fixing energy rather than the usual parameters.

Findings

Successfully determines ground state properties at fixed energy.

Provides a new perspective on quantum Monte Carlo simulations.

Enables analysis of Hamiltonians with fixed ground state energy.

Abstract

In this paper we explore new ways to study the zero temperature limit of quantum statistical mechanics using Quantum Monte Carlo simulations. We develop a Quantum Monte Carlo method in which one fixes the ground state energy as a parameter. The Hamiltonians we consider are of the form $H=H_{0}+\lambda V$ with ground state energy E. For fixed $H_{0}$ and V, one can view E as a function of $\lambda$ whereas we view $\lambda$ as a function of E. We fix E and define a path integral Quantum Monte Carlo method in which a path makes no reference to the times (discrete or continuous) at which transitions occur between states. For fixed E we can determine $\lambda(E)$ and other ground state properties of H.