ISING-MODEL DESCRIPTION OF QUANTUM CRITICAL POINTS IN 1D ELECTRON AND SPIN SYSTEMS

摘要

In these lectures, we have discussed a nonperturbative description of the Ising criticality in the DSG model (4.1). Using the equivalence be ween the DSG model and a deformed quantum Ashkin-Teller model, valid in the vicinity of the decoupling point, β~2 = 4π, we were able to identify the effective Ising degrees of freedom that asymptotically decouple from the rest of the spectrum and become critical in the infrared limit. This identification allowed us to describe the UV-IR "transmutation" of all physical fields of the DSG model. We have also demonstrated the efficiency ot our approach to describe Ising transitions in some physical realizations of the DSG model. The quantum-Ising-chain approach can be generalised to the case when the number of the constituent Ising models, coup ed by the interaction h ∏_j σ_j, is larger than 2. Such situation can indeed be realized in certain SU(2)-invariant spin-ladders models which can be driven to criticality under the action of external staggered fields. In such systems, the quantum critical points may be not only of the Ising type but also correspond to SU(2)_κ WZNW universality class. Such examples will be considered elsewhere.