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\(XXZ\) Spin-Peierls Chain

Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

The phase transition and the phase diagram between the adiabatic and antiadiabatic limits in the spin-Peierls model will be investigated in this chapter. As we explained in Chap.  3, the conventional quantum Monte Carlo methods cannot efficiently calculate the model. Then, for overcoming the difficulty, we will apply the new Monte Carlo update techniques and the analysis that we developed in Chap.  2 4. We will show the precise transition point and the universality class of the spin-Peierls chain without any approximation, which has been discussed for several decades. For the XY anisotropic case, the Kosterlitz-Thouless type phase transition occurs between the Tomonaga-Luttinger liquid phase and the dimer (spin-Peierls) phase. For the Ising anisotropic case, on the other hand, the phase transition between the Néel phase and the dimer phase is the Gaussian universality. The whole phase diagram will be shown, compared to the previous result from the renormalization group method. We will discuss the correspondence that the phase diagram is consistent with the J1-J2 model that is an effective spin model in the antiadiabatic limit; that is the quantum nature of the lattice degree of freedom is relevant to the phase diagram.

Keywords

Kosterlitz-Thouless transition \(J_1-J_2\) spin chain model Sine-Gordon model Adiabatic-antiadiabatic crossover 

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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Department of PhysicsBoston UniversityBostonUSA

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