Gr{\"u}neisen parameter of quantum magnets with spin gap

TL;DR

This paper derives analytical expressions for thermodynamic quantities, including the Grüneisen parameter, in spin gapped quantum magnets using the Hartree-Fock-Bogoliubov approach, revealing critical behavior near phase transitions.

Contribution

It introduces a novel analytical framework for calculating thermodynamic properties of triplons in quantum magnets, highlighting differences from previous approaches and predicting divergence behaviors.

Findings

Discontinuous change in Grüneisen parameter at critical temperature.

Divergence of Grüneisen parameter near quantum critical point.

Sign change of Grüneisen parameter across Bose-Einstein condensation.

Abstract

Using Hartree-Fock-Bogoliubov (HFB) approach we obtained analytical expressions for thermodynamic quantities of the system of triplons in spin gapped quantum magnets such as magnetization, heat capacity and the magnetic Gr{\"u}neisen parameter $\Gamma_H$. Near the critical temperature, $\Gamma_H$ is discontinuous and changes its sign upon the Bose-Einstein condensation (BEC) of triplons. On the other hand, in the widely used Hartree-Fock-Popov (HFP) approach there is no discontinuity neither in the heat capacity nor in the Gr{\"u}neisen parameter. We predict that in the low-temperature limit and near the critical magnetic field $H_c$, $\Gamma_H$ diverges as $\Gamma_H\sim 1/T^{2}$, while it scales as $\Gamma_H\sim 1/(H-H_c)$ as the magnetic field approaches the quantum critical point at $H_c$.