The finite-temperature binary collision method for treating spin-dimer systems: Taking TlCuCl3 as an example

We showed that the bond-operator Hamiltonian for spin-dimer systems above the critical field is equivalent to a single-field (effective) Hamiltonian with finite coupling strength. This equivalence is revealed by going beyond the mean field level of the singlet operator and through an orthogonal transformation. The associated field operator, named as the effective magnon in this single-field Hamiltonian, is the linear combination of the hard-core triplet magnons. The magnetic properties and condensation of spin dimers are ascribed to the behaviors of effective magnons. By recognizing the effective coupling of the Hamiltonian for hard-core effective magnons as the sum of the T-dependent ladder diagrams with hard-core vertex, we study the finite-temperature behaviors of spin-dimer systems in both condensed and noncondensed phases. We calculate excitation spectra, energy gaps, and the parallel and transverse (staggered) magnetizations at finite temperatures. Our results, which are improvements on the ordinary Hartree–Fock–Popov approximation, are consistent with experiments and numerical results. - Highlights: ► The bond-operator Hamiltonian for dimers above Hc is equivalent to a single-field one. ► The effective Hamiltonian for spin dimers can be identified as a renormalized one. ► Finite-T coupling is constructed by summing finite-T ladder diagrams. ► The effective Hamiltonian with finite-T coupling is better for hard-core systems at T>0.