Monte Carlo Hamiltonian: Generalization to Quantum Field Theory

TL;DR

This paper extends the Monte Carlo Hamiltonian method to quantum field theory and many-body systems, demonstrating its effectiveness with Klein-Gordon field theory as a test case.

Contribution

The paper introduces a generalized Monte Carlo Hamiltonian approach applicable to quantum field theory, overcoming limitations of traditional methods in excited state computations.

Findings

Successfully applied to Klein-Gordon field theory

Demonstrated improved excited state calculations

Extended applicability to many-body systems

Abstract

Monte Carlo techniques with importance sampling have been extensively applied to lattice gauge theory in the Lagrangian formulation. Unfortunately, it is extremely difficult to compute the excited states using the conventional Monte Carlo algorithm. Our recently developed approach: the Monte Carlo Hamiltonian method, has been designed to overcome the difficulties of the conventional approach. In this paper, we extend the method to many body systems and quantum field theory. The Klein-Gordon field theory is used as a testing ground.