Thermodynamics of the quantum Ising model in the two-dimensional kagome lattice

In the classical Ising model on the kagome lattice, there are macroscopically degenerate classical states with exponentially decayed spin correlation. As the singular quantum perturbation is introduced by applying the transverse magnetic field, the quantum ground state remains disordered, dubbed by “disorder by disorder.” Here, we compute the temperature dependence of the spin susceptibility and the specific heat for different strengths of the field to understand the effect of the singular quantum perturbation in this system. The relevance to the $\mathrm{Zn}{\mathrm{Cu}}_3{\left(\mathrm{O}\mathrm{H}\right)}_6{\mathrm{Cl}}_2$ will be also commented.

Figure 1

(Color online) The temperature (in the unit of $J$) dependence of the inverse of the ${\chi }_{zz}$ per spin. $L=2,4,6$ correspond to $N=12,48,108$, respectively. The blue straight line is the Curie-Weiss fit. QMC is denoted for the result from quantum Monte Carlo and ED is the one from exact diagonalization

Figure 2

(Color online) The magnifying plot around the origin of Fig. 1. At $\Gamma =0$ (classical disorder), the longitudinal susceptibility diverges at $T=0$. At finite $\Gamma$ (quantum disorder), they saturate at finite values at $T=0$. (Temperature is in the unit of $J$.)

Figure 3

(Color online) The temperature dependence of the inverse of the powder susceptibility $\chi$ per spin. $L=2,4,6$ correspond to $N=12,48,108$, respectively. The blue straight line is the Curie-Weiss fit. QMC is denoted for the result from quantum Monte Carlo, and ED is the one from exact diagonalization. (Temperature is in the unit of $J$.)

Figure 4

(Color online) The magnifying plot around the origin of Fig. 3. At $\Gamma =0$ (classical disorder), the powder susceptibility diverges at $T=0$. At finite $\Gamma$ (quantum disorder), they saturate at finite values at $T=0$. (Temperature is in the unit of $J$.)

Figure 5

(Color online) The temperature (in the unit of $J$) dependence of specific heat per spin. $L=6$ corresponds to $N=108$. QMC is denoted for the result from quantum Monte Carlo, and ED is the one from exact diagonalization