Multiple-particle interaction in $1+1$ dimensional lattice model

Abstract

Finite volume multiple-particle interaction is studied in a two-dimensional complex ${\varphi }^4$ lattice model. The existence of analytical solutions to the ${\varphi }^4$ model in two-dimensional space and time makes it a perfect model for the numerical study of finite volume effects of multi-particle interaction. The spectra from multiple particles are extracted from the Monte Carlo simulation on various lattices in several moving frames. The $S$-matrix of multi-particle scattering in ${\varphi }^4$ theory is completely determined by two fundamental parameters: single particle mass and the coupling strength of two-to-two particle interaction. These two parameters are fixed by studying single-particle and two-particle spectra. Due to the absence of the diffraction effect in the ${\varphi }^4$ model, three-particle quantization conditions are given in a simple analytical form. The three-particle spectra from simulation show remarkable agreement with the prediction of exact solutions.

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• Three-body interactions from the finite-volume QCD spectrum
• The energy-dependent ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ scattering amplitude from QCD
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• $DDK$ system in finite volume
• Relativistic-invariant formulation of the NREFT three-particle quantization condition
• Relativistic $N$-particle energy shift in finite volume
• Three-body dynamics of the $a_1(1260)$ resonance from lattice QCD
• Multi-${\pi }^{+}$ systems in finite volume
• Modeling few-body resonances in finite volume
• A lattice model of heavy-light three-body system
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• Coulomb corrections to two-particle interaction in artificial traps
• Charged particles interaction in both a finite volume and a uniform magnetic field
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• Threshold expansion formula of $N$-boson in finite volume from variational approach
• Nuclear reactions in artificial traps
• Particle-dimer approach for the Roper resonance in a finite volume
• Finite-volume energy shift of the three-nucleon ground state
• Charged particles interaction in both a finite volume and a uniform magnetic field II: topological and analytic properties of a magnetic system
• Spurious poles in a finite volume
• Toward extracting scattering phase shift from integrated correlation functions on quantum computers
• Transmission coefficient of interacting few-body system in one dimensional space