Thermodynamical Observables in a Finite Temperature Window from the Monte Carlo Hamiltonian

TL;DR

This paper introduces the Monte Carlo Hamiltonian, a stochastic method to compute low-energy spectra and thermodynamical observables in many-body systems within a finite energy and temperature window, demonstrated on a lattice field theory model.

Contribution

The paper presents a novel Monte Carlo Hamiltonian approach that constructs an effective Hamiltonian from classical action to analyze low-energy and low-temperature properties.

Findings

Successfully computes energy spectrum and wave functions in a low energy window.

Enables calculation of thermodynamical observables at low temperatures.

Demonstrated on a Klein-Gordon lattice field theory model.

Abstract

The Monte Carlo (MC) Hamiltonian is a new stochastic method to solve many-body problems. The MC Hamiltonian represents an effective Hamiltonian in a finite energy window. We construct it from the classical action via Monte Carlo with importance sampling. The MC Hamiltonian yields the energy spectrum and corresponding wave functions in a low energy window. This allows to compute thermodynamical observables in a low temperature window. We show the working of the MC Hamiltonian by an example from lattice field theory (Klein-Gordon model).