Tan's contact for bosonic systems with a fixed chemical potential

The temperature dependence of Tan’s contact parameter C and its derivatives for spin gapped

quantum magnets are investigated.We use the paradigm of Bose–Einstein condensation

(BEC) to describe the low temperature properties of quasiparticles in the system known as

triplons. Since the number of particles and the condensate fraction are not fixed we use the

μVT ensemble to calculate the thermodynamic quantities. The interactions are treated at the

Hartree–Fock–Bogoliubov approximation level. We obtained the temperature dependence of

C and its derivative with respect to temperature and applied magnetic field both above and

below Tc of the phase transition from the normal phase to BEC. We have shown that C is

regular, while its derivatives are discontinuous at Tc. Moreover, we have found a sign change in ∂C/∂T close to

the critical temperature. As to the quantum critical point, C and its derivatives are regular as a

function of the control parameter r, which induces the quantum phase transition. At very low

temperatures, one may evaluate C has a simple expression where only the

effective mass of quasiparticles needs to be estimated. We propose a method for

measuring of Tan’s contact for spin gapped dimerized magnets.