Dear friends, here I am going to share XXZ Chain Correlation Functions in PDF form for all of you. The purpose of this chapter is to focus on two models fundamental to the study of both 1d quantum systems and 2d classical systems. They are the XXZ chain (and its 2d classical analogue, the six-vertex model), and the 2d classical rotor or “XY” model. The XXZ model is a deformation of the Heisenberg model breaking the SU(2) symmetry down to a U(1) subgroup.
The degrees of freedom of the XY model is classical fixed length “spins” pointing anywhere in a plane, and so can be represented by an angle 0 ≤ θ < 2π. The latter also has a U(1) symmetry given by shifting θ by a constant mod 2π. The physics of the two models are closely related; in fact, in a sense to be described precisely, it is identical. Both are worth studying in their own right.
From the physics point of view, the rotor model describes for example the transition in superfluids: the value θ is the phase of the expectation value of the wave function. Even though the existence of superfluids of course is a quantum-mechanical effect, quantum effects are essentially negligible when studying the transition between the superfluid and the normal phase.
Thus the classical rotor model provides a way of quantitatively understanding this transition. Physically, the XXZ chain is one of the simplest models of a magnet. The free parameter describing the anisotropy (the breaking of rotational symmetry in spin space) also provides a very useful tool in describing the behaviour; one can continuously tune in between ferromagnets and antiferromagnetic.
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XXZ Chain Correlation Functions PDF