Asymptotic scattering and duality in the one-dimensional three-state quantum Potts model on a lattice

Abstract

We determine numerically the single-particle and the two-particle spectrum of the three-state quantum Potts model on a lattice by using the density matrix renormalization group method, and extract information on the asymptotic (small momentum) S-matrix of the quasiparticles. The low energy part of the finite size spectrum can be understood in terms of a simple effective model introduced in a previous work, and is consistent with an asymptotic S-matrix of an exchange form below a momentum scale $p^{\ast }$. This scale appears to vanish faster than the Compton scale, $mc$, as one approaches the critical point, suggesting that a dangerously irrelevant operator may be responsible for the behavior observed on the lattice.

final version, 25 pages, 15 eps figures

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• Excitation spectrum and Density Matrix Renormalization Group iterations
• Adiabatic Tracking of a State: a New Route to Nonequilibrium Physics
• Relaxation and entropy generation after quenching quantum spin chains
• Critical properties of quantum three- and four-state Potts models with boundaries polarized along the transverse field
• Radiative corrections to the quark masses in the ferromagnetic Ising and Potts field theories
• Quasi-particle spectrum and entanglement generation after a quench in the quantum Potts spin chain
• Spin fluctuations after quantum quenches in the S=1 Haldane chain: numerical validation of the semi-semiclassical theory
• Imaginary-Temperature Zeros for Quantum Phase Transitions
• Confinement and false vacuum decay on the Potts quantum spin chain
• Finite volume analysis of scattering theory in the scaling Potts model