Dynamical correlations and quantum phase transition in the quantum Potts model

Abstract

We present a detailed study of the finite temperature dynamical properties of the quantum Potts model in one dimension.Quasiparticle excitations in this model have internal quantum numbers, and their scattering matrix {\gf deep} in the gapped phases is shown to take a simple {\gf exchange} form in the perturbative regimes. The finite temperature correlation functions in the quantum critical regime are determined using conformal invariance, while {\gf far from the quantum critical point} we compute the decay functions analytically within a semiclassical approach of Sachdev and Damle [K. Damle and S. Sachdev, Phys. Rev. B \textbf{57}, 8307 (1998)]. As a consequence, decay functions exhibit a {\em diffusive character}. {\gf We also provide robust arguments that our semiclassical analysis carries over to very low temperatures even in the vicinity of the quantum phase transition.} Our results are also relevant for quantum rotor models, antiferromagnetic chains, and some spin ladder systems.

18 PRB pages added corrections

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• Finite Temperature Dynamical Structure Factor of Alternating Heisenberg Chains
• Low-Temperature Dynamical Structure Factor of the Two-Leg Spin-1/2 Heisenberg Ladder
• Semi-classical theory for quantum quenches in the O(3) non-linear sigma model
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• Quasi Long Range Order and Vortex Lattice in the Three State Potts Model
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• Finite volume analysis of scattering theory in the scaling Potts model
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• Quench dynamics and statistics of measurements for a line of quantum spins in two dimensions