Monte Carlo Hamiltonian

Jirari, H.; Kröger, H.; Luo, Xiang-Qian; Moriarty, K.J.M.

doi:10.1016/s0375-9601(99)00304-7

Cited by 25 publications

(50 citation statements)

References 10 publications

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“…For fermions, the calculation is far from trivial. Recently we proposed a Monte Carlo technique in the Hamiltonian formulation [20] for the purpose to do nonperturbative numerical simulations, by combining the virtues of the Monte Carlo algorithm with importance sampling and the Hamiltonian approach. We hope to apply it to QCD and with the aim to obtain useful information for RHIC physics.…”

Section: Discussionmentioning

confidence: 99%

Hamiltonian lattice quantum chromodynamics at finite chemical potential

Gregory¹,

Guo²,

Kröger

et al. 2000

Phys. Rev. D

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At sufficiently high temperature and density, quantum chromodynamics (QCD) is expected to undergo a phase transition from the confined phase to the quark-gluon plasma phase. In the Lagrangian lattice formulation the Monte Carlo method works well for QCD at finite temperature, however, it breaks down at finite chemical potential. We develop a Hamiltonian approach to lattice QCD at finite chemical potential and solve it in the case of free quarks and in the strong coupling limit. At zero temperature, we calculate the vacuum energy, chiral condensate, quark number density and its susceptibility, as well as mass of the pseudoscalar, vector mesons and nucleon. We find that the chiral phase transition is of first order, and the critical chemical potential is µ C = m (0) dyn (dynamical quark mass at µ = 0). This is consistent with µ C ≈ M (0) N /3 (where M (0) N is the nucleon mass at µ = 0). *

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Section: Discussionmentioning

confidence: 99%

Hamiltonian lattice quantum chromodynamics at finite chemical potential

Gregory¹,

Guo²,

Kröger

et al. 2000

Phys. Rev. D

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“…It is the objective of this article to construct such measure. Physical scenarios which require the calculation of single amplitudes are: amplitudes of decay reactions, the partition function Z(β), the free energy F (β) given in terms of the partition function, or matrix elements involved in the construction of the Monte Carlo Hamiltonian [1,2].…”

Section: < ω T = +∞|ô[U ]|ω T = −∞ >= [Du ]ô[U ]] Exp[−s[u ]/ ] [Dumentioning

confidence: 99%

Measure of the path integral in lattice gauge theory

et al. 2005

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We show how to construct the measure of the path integral in lattice gauge theory. This measure contains a factor beyond the standard Haar measure. Such factor becomes relevant for the calculation of a single transition amplitude (in contrast to the calculation of ratios of amplitudes). Single amplitudes are required for computation of the partition function and the free energy. For U (1 ) lattice gauge theory, we present a numerical simulation of the transition amplitude comparing the path integral with the evolution in terms of the Hamiltonian, showing good agreement.

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“…Let's review briefly the basic ideas [1]. According to Feynman's path integral approach to QM, the (imaginary time) transition amplitude between an initial state at position x i , and time t i , and final state at x f , t f is related to the Hamiltonian H by…”

Section: Algorithmmentioning

confidence: 99%

“…Recently, we proposed an algorithm to compute the MC Hamiltonian [1]. The advantage, in comparison with the standard Lagrangian MC approach, is that one can obtain not only the spectrum of ground and excited states, but also the wave functions.…”

Section: Introductionmentioning

confidence: 99%

“…The advantage, in comparison with the standard Lagrangian MC approach, is that one can obtain not only the spectrum of ground and excited states, but also the wave functions. The method has been tested in quantum mechanics (QM) in 1+1 dimensions, where the exact results were reproduced with high precision [1][2][3]. In this paper, we apply this algorithm to QM in 2+1 dimensions.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Theory with Many Degrees of Freedom from Monte Carlo Hamiltonian

Luo¹

2000

Nuclear Physics B - Proceedings Supplements

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With our recently proposed effective Hamiltonian via Monte Carlo, we are able to compute low energy physics of quantum systems. The advantage is that we can obtain not only the spectrum of ground and excited states, but also wave functions. The previous work has shown the success of this method in (1+1)-dimensional quantum mechanical systems. In this work we apply it to higher dimensional systems.

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Monte Carlo Hamiltonian

Cited by 25 publications

References 10 publications

Hamiltonian lattice quantum chromodynamics at finite chemical potential

Hamiltonian lattice quantum chromodynamics at finite chemical potential

Measure of the path integral in lattice gauge theory

Quantum Theory with Many Degrees of Freedom from Monte Carlo Hamiltonian

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