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 γis small, e.g., ΔT_c \approx 10%$ of Tc in H = 6T and for γ\approx 4 μeV.

arXiv commentRevised version

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• Gr{ü}neisen parameter of quantum magnets with spin gap
• Self-consistent theory of a homogeneous binary Bose mixture with strong repulsive interspecies interaction
• Spin-gapped magnets with weak anisotropies I: Constraints on the phase of the condensate wave function
• Effects of exchange and weak Dzyaloshinsky-Moriya anisotropies on thermodynamic characteristics of spin-gapped magnets
• Critical behavior of Tan's contact for bosonic systems with a fixed chemical potential
• Characteristic temperatures of a triplon system of dimerized quantum magnets
• Hugenholtz -- Pines relations and the critical temperature of a Rabi coupled binary Bose system
• Defining a critical temperature of a crossover from BEC to the normal phase in anisotropic quantum magnets