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Lattice Boltzmann method for quantum field theory [PDF]

Journal of Physics A: Mathematical and Theoretical, 2007
It is shown that a (1 + 1)-dimensional lattice Boltzmann discretization of the Klein–Gordon and Dirac equations complies with equal-time-commutation-relations. As a result, the lattice Boltzmann discretization leads to a consistent lattice formulation of the quantum field theory in 1 + 1 dimensions.
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Sign Problems in Quantum Field Theory: Classical and Quantum Approaches

, 2020
Monte Carlo calculations in the framework of lattice field theory provide non-perturbative access to the equilibrium physics of quantum fields. When applied to certain fermionic systems, or to the calculation of out-of-equilibrium physics, these methods ...
S. Lawrence
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Quantum Field Theory (QFT) on the Lattice

2016
In 1964, Gell-Mann [1] and Zweig [2] proposed that hadrons, the particles which experience strong interactions, are made of quarks. Quarks are confined within hadrons and never seen in isolation. Electron-nucleon scattering experiments at large momentum transfer could be explained by assuming the nucleon is made of almost-free point-like constituents ...
Francesco Knechtli, Michael Günther, Mike Peardon   +2 more
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Quantum tetrahedral mean-field theory of the pyrochlore lattice

Canadian Journal of Physics, 2001
A quantum mean-field theory of the pyrochlore lattice is presented. The starting point is not the individual magnetic ions, as in the usual Curie-Weiss mean-field theory, but a set of interacting corner-sharing tetrahedra. We check the consistency of the model against magnetic susceptibility data and find a good agreement between the theoretical ...
D. L. Huber, Angel J. Garcia-Adeva
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MCMC and Quantum Field Theories on a Lattice

2020
We can consider relativistic quantum field theory as the quantum mechanics of fields defined on a spacetime. A field has infinite number of degrees of freedom since it can take a value at every point in spacetime.
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Lower bounds for quantum Hamiltonians in lattice field theories

Physical Review D, 1978
A method for approximately including quantum effects on the solution to lattice field theories is presented. The formalism is an extension of the semiquantum approximation of Sachrajda, Weldon, and Blankenbecler to obtain lower bounds for quantum Hamiltonians. This approach yields classical-like equations in which the effects of quantum fluctuations is
Richard Blankenbecler, José R. Fulco
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Quantum theory of an antiferromagnet on a triangular lattice in a magnetic field

Journal of Physics: Condensed Matter, 1991
The reorientation process in a magnetic field in two-dimensional isotropic and XY quantum Heisenberg antiferromagnets is shown to occur through the intermediate phase with unbroken continuous symmetry and constant magnetization equal to one third of the saturation value.
A V Chubokov, D I Golosov
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Lattice fractional quantum field theory: Exact differences approach

Modern Physics Letters A, 2020
An approach, which is based on exact fractional differences, is used to formulate a lattice fractional field theories on unbounded lattice spacetime. An exact discretization of differential and integral operators of integer and non-integer orders is suggested.
Vasily E. Tarasov, Vasily E. Tarasov
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A quantum field theory of melting and lattice dynamics

Physica A: Statistical Mechanics and its Applications, 1986
Abstract The melting and the lattice dynamics are investigated from the view-point of a quantum field theory at finite temperature (thermo field theory). Our theory starts with ion cores and valence electrons interacting with each other as the first principle.
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