Integrability, Non-integrability and confinement

Abstract

We discuss the main features of quantum integrable models taking the classes of universality of the Ising model and the repulsive Lieb-Liniger model as paradigmatic examples. We address the breaking of integrability by means of two approaches, the Form Factor Perturbation Theory and semiclassical methods. Each of them has its own advantage. Using the first approach, one can relate the confinement phenomena of topological excitations to the semi-locality of the operator which breaks integrability. Using the second approach, one can control the bound states which arise in each phase of the theory and predict that their number cannot be more than two.

Invited talk at StatPhys24, Cairns (Australia) 2010. 27 pages, 16 figures

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Cited by in corpus (9)

• Real time confinement following a quantum quench to a non-integrable model
• Confinement and Entanglement Dynamics on a Digital Quantum Computer
• Collisions of false-vacuum bubble walls in a quantum spin chain
• Baryon masses in the three-state Potts field theory in a weak magnetic field
• The effect of optical lattice heating on the momentum distribution of a 1D Bose gas
• Spinon confinement in the gapped antiferromagnetic XXZ spin-1/2 chain
• Fractionalized holes in one-dimensional ${\mathbb{Z}}_2$ gauge theory coupled to fermion matter -- deconfined dynamics and emergent integrability
• Soliton confinement in the double sine-Gordon model
• Confinement in the tricritical Ising model