In order to solve quantum field theory in a non-perturbative way, Lagrangian lattice simulations have been very successful. Here we discuss a recently proposed alternative Hamiltonian lattice formulation - the Monte Carlo Hamiltonian. In order to show its working in the case of the scalar $Φ^{4}_{1+1}$ model, we have computed thermodynamic functions like free energy, average energy, entropy and specific heat. We find good agreement between the results from the Monte Carlo Hamiltonian and standard Lagrangian lattice computations. However, the Monte Carlo Hamiltonian results show less fluctuations under variation of temperature. We address properties of the MC Hamiltonian, like a finite temperature window, and scaling properties. Also we discuss possible future applications - like quantum chaos in many-body systems, the non-perturbative computation of wave functions of elementary particles, as well as scattering amplitudes in high energy physics.In order to solve quantum field theory in a non-perturbative way, Lagrangian lattice simulations have been very successful. Here we discuss a recently proposed alternative Hamiltonian lattice formulation - the Monte Carlo Hamiltonian. In order to show its working in the case of the scalar $Φ^{4}_{1+1}$ model, we have computed thermodynamic functions like free energy, average energy, entropy and specific heat. We find good agreement between the results from the Monte Carlo Hamiltonian and standard Lagrangian lattice computations. However, the Monte Carlo Hamiltonian results show less fluctuations under variation of temperature. We address properties of the MC Hamiltonian, like a finite temperature window, and scaling properties. Also we discuss possible future applications - like quantum chaos in many-body systems, the non-perturbative computation of wave functions of elementary particles, as well as scattering amplitudes in high energy physics.

arXiv:hep-lat/0301012Jan 13, 20031 citation

Thermodynamics from Monte Carlo Hamiltonian

Caron, L. A., H. Kröger, G. Melkonyan +2 more

We construct an effective low-energy Hamiltonian from the classical action via Monte Carlo with importance sampling. We use Monte Carlo (i) to compute matrix elements of the transition amplitude and (ii) to construct stochastically a basis. The MC Hamiltonian allows to obtain energies and wave functions of low-lying states. It allows also to compute thermodynamical observables in some temperature window (starting from temperature zero). We present examples from lattice field theory (Klein-Gordon model).We construct an effective low-energy Hamiltonian from the classical action via Monte Carlo with importance sampling. We use Monte Carlo (i) to compute matrix elements of the transition amplitude and (ii) to construct stochastically a basis. The MC Hamiltonian allows to obtain energies and wave functions of low-lying states. It allows also to compute thermodynamical observables in some temperature window (starting from temperature zero). We present examples from lattice field theory (Klein-Gordon model).

arXiv:hep-lat/0202016Feb 11, 20021 citation

Φ^{4}_{1+1}

model, we have computed thermodynamic functions like free energy, average energy, entropy and specific heat. We find good agreement between the results from the Monte Carlo Hamiltonian and standard Lagrangian lattice computations. However, the Monte Carlo Hamiltonian results show less fluctuations under variation of temperature. We address properties of the MC Hamiltonian, like a finite temperature window, and scaling properties. Also we discuss possible future applications - like quantum chaos in many-body systems, the non-perturbative computation of wave functions of elementary particles, as well as scattering amplitudes in high energy physics.