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 γ is small, e.g., of Tc in H = 6 T and for .
Highlights
Spontaneous symmetry breaking (SSB) plays an important role in particle and condensed matter physics
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 Bose–Einstein condensation (BEC) scenario is still valid
Assuming that the low temperature properties of quantum magnets with a weak U(1) symmetry breaking can be described in a BEC—like scenario, we proposed a new mean-field approaches (MFA) based approach within the Hartree–Fock– Bogolyubov approximation, which takes into account an anomalous density σ and exchange anisotropy (EA)
Summary
This work must maintain Einstein condensation (BEC) of magnetic quasiparticles (triplons). Some mean-field approaches attribution to the author(s) and the title of (MFA) to describe these systems, based on the standard grand canonical ensemble, do not take the the work, journal citation and DOI. An explicit breaking of the U(1) symmetry as observed, for example, in TlCuCl3 makes the application of MFA more complicated. 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.
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