Title: Bose - Einstein condensation of triplons with a weakly broken U(1) symmetry,
Abstract: The low-temperature properties of certain quantum magnets can be described in
terms of a Bose-Einstein condensation (BEC) of magnetic quasiparticles
(triplons). Some mean-field approaches (MFA) to describe these systems, based
on the standard grand canonical ensemble, do not take the anomalous density
into account and leads to an internal inconsistency, as it has been shown by
Hohenberg and Martin, and may therefore produce unphysical results. Moreover,
an explicit breaking of the U(1) symmetry as observed, for example, in TlCuCl3
makes the application of MFA more complicated. In the present work, we develop
a self-consistent MFA approach, similar to the Hartree-Fock-Bogolyubov
approximation in the notion of representative statistical ensembles, including
the effect of a weakly broken U(1) symmetry. We apply our results on
experimental data of the quantum magnet TlCuCl3 and show that magnetization
curves and the energy dispersion can be well described within this
approximation assuming that the BEC scenario is still valid. We predict that
the shift of the critical temperature Tc due to a finite exchange anisotropy is
rather substantial even when the anisotropy parameter \gamma is small, e.g.,
\Delta T_c \approx 10%$ of Tc in H = 6T and for \gamma\approx 4 \mu eV.