Monte Carlo Hamiltonian – from statistical physics to quantum theory

Melkonyan³

et al. 2011

Mod. Phys. Lett. A

We address an old problem in lattice gauge theory -the computation of the spectrum and wave functions of excited states. Our method is based on the Hamiltonian formulation of lattice gauge theory. As strategy, we propose to construct a stochastic basis of Bargmann link states, drawn from a physical probability density distribution. Then we compute transition amplitudes between stochastic basis states. From a matrix of transition elements we extract energy spectra and wave functions. We apply this method to U(1) 2+1 lattice gauge theory. We test the method by computing the energy spectrum, wave functions and thermodynamical functions of the electric Hamiltonian of this theory and compare them with analytical results. We observe a reasonable scaling of energies and wave functions in the variable of time. We also present first results on a small lattice for the full Hamiltonian including the magnetic term.

Section: Exp[−h T/h] |ξ ∼ Lim T→∞ Exp[−e Gr T/h]|ω ω|ξ (2)supporting

confidence: 79%

SPECTRUM AND WAVE FUNCTIONS OF U(1)₂₊₁ LATTICE GAUGE THEORY FROM MONTE CARLO HAMILTONIAN

Hosseinizadeh

Melkonyan³

et al. 2011

Mod. Phys. Lett. A

“…Some years ago, we proposed a new approach [24] (named Monte Carlo Hamiltonian method or MCH) to investigate this problem. A lot of models [24,28,29,30,31,32,33,34] in QM have been used to test the method. This method has also been applied to scalar field theories [35,36,37,38].…”

Section: Monte Carlo Hamiltonianmentioning

confidence: 99%

Bound states and critical behavior of the Yukawa potential

Luo

2006

SCI CHINA SER G

Self Cite

We investigate the bound states of the Yukawa potential V (r) = −λ exp(−αr)/r, using different algorithms: solving the Schrödinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical α = α C , above which no bound state exists. We study the relation between α C and λ for various angular momentum quantum number l, and find in atomic units, α C (l) = λ[A 1 exp(−l/B 1 ) + A 2 exp(−l/B 2 )], with A 1 = 1.020(18), B 1 = 0.443(14), A 2 = 0.170(17), and B 2 = 2.490(180).

“…[6]. Carrying out these steps allows to construct an effective Hamiltonian, which has turned out to reproduce well low energy physics of a lot of quantum systems [6,7,8,9,10,11,12,13,14,15,16,17].…”

Section: Matrix Elementsmentioning

confidence: 99%

“…its spectrum and eigen states. A lot of models [6,7,8,9,10,11,12,13] in quantum mechanics (QM) have been used to test the method. This method has also been applied to scalar field theories [14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo Hamiltonian: Inverse Potential

Luo¹,

Xiaoni²,

2004

Commun. Theor. Phys.

Self Cite

The Monte Carlo Hamiltonian method developed recently allows to investigate ground state and low-lying excited states of a quantum system, using Monte Carlo algorithm with importance sampling. However, conventional MC algorithm has some difficulties when applying to inverse potentials. We propose to use effective potential and extrapolation method to solve the problem. We present examples from the hydrogen system.