Studying the perturbed Wess–Zumino–Novikov–Witten SU (2) k theory using the truncated conformal spectrum approach
R.M. Konik (Department of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, NY, 11973-5000, USA); T. Pálmai (MTA-BME “Momentum” Statistical Field Theory Research Group, Budafoki út 8, Budapest, H-1111, Hungary)
; G. Takács (MTA-BME “Momentum” Statistical Field Theory Research Group, Budafoki út 8, Budapest, H-1111, Hungary, Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, Budafoki út 8, Budapest, H-1111, Hungary); A.M. Tsvelik (Department of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, NY, 11973-5000, USA)
We study the SU(2)k Wess–Zumino–Novikov–Witten (WZNW) theory perturbed by the trace of the primary field in the adjoint representation, a theory governing the low-energy behavior of a class of strongly correlated electronic systems. While the model is non-integrable, its dynamics can be investigated using the numerical technique of the truncated conformal spectrum approach combined with numerical and analytical renormalization groups (TCSA + RG). The numerical results so obtained provide support for a semiclassical analysis valid at k≫1 . Namely, we find that the low energy behavior is sensitive to the sign of the coupling constant, λ . Moreover, for λ>0 this behavior depends on whether k is even or odd. With k even, we find definitive evidence that the model at low energies is equivalent to the massive O(3) sigma model. For k odd, the numerical evidence is more equivocal, but we find indications that the low energy effective theory is critical.
