U(1)symmetry breaking and violated axial symmetry inTlCuCl3and other insulating spin systems

Abstract

We describe the Bose-Einstein condensate of magnetic bosonic quasiparticles in insulating spin systems using a phenomenological standard functional method for $T=0$. We show that results that are already known from advanced computational techniques immediately follow. The inclusion of a perturbative anisotropy term that violates the axial symmetry allows us to remarkably well explain a number of experimental features of the dimerized spin-1/2 system ${\text{TlCuCl}}_{3}$. Based on an energetic argument we predict a general intrinsic instability of an axially symmetric magnetic condensate toward a violation of this symmetry, which leads to the spontaneous formation of an anisotropy gap in the energy spectrum above the critical field. We, therefore, expect that a true Goldstone mode in insulating spin systems, i.e., a strictly linear energy-dispersion relation down to arbitrarily small excitations energies, cannot be observed in any real material.