Quantum phase transition in spin-$\frac{1}{2}$ XX Heisenberg chain with three-spin interaction

The quantum phase transition in the spin-$\frac{1}{2}$ XX Heisenberg chain model with three-spin interaction is studied. Using the Jordan-Wigner transformation, several thermodynamic, as well as thermal and spin transport quantities of the system are calculated exactly. It is shown that the three-spin interaction influences the calculated quantities and leads to characteristic features of the quantum phase transition. The effects of a finite magnetic field on the magnetic moment and magnetic susceptibility are also discussed.

Figure 1

The ground state energy $E_0\left(\alpha \right)∕NJ$ and the generalized stiffness $\eta \left(\alpha \right)∕NJ$ versus the parameter $\alpha$.

Figure 2

The spinless fermion density of states $\rho (\omega ,\alpha )J$ versus the scaled energy $\omega ∕J$ for different values of $\alpha$.

Figure 3

The specific heat of the system $C(T,\alpha )$ versus the scaled temperature $T∕J$ for different values of $\alpha$.

Figure 4

The magnetic susceptibility of the system $\chi (T,\alpha )J$ versus the scaled temperature $T∕J$ for different values of $\alpha$. The inset shows $\chi \left(\alpha \right)J$ versus $\alpha$ at $T=0$.

Figure 5

The entropy $S(\alpha ,T)$ of the system versus the parameter $\alpha$ at $T=0.0001J$.

Figure 6

The short-range orders ${\rho }_{l,l+m}\left(\alpha \right)$ of the system for $m=1$, 2, and 3 are plotted versus the parameter $\alpha$ at $T=0$.

Figure 7

Spin Drude weight $D_S(T,\alpha )∕J$ versus the scaled temperature $T∕J$ for different values of $\alpha$. The inset shows $D_S\left(\alpha \right)∕J$ versus $\alpha$ at $T=0$.

Figure 8

Thermal Drude weight $D_E(T,\alpha )∕J^2$ versus the scaled temperature $T∕J$ for different values of $\alpha$. For easier comparison, the inset shows $D_E\left(\alpha \right)∕JT$ versus $T∕J$ for different $\alpha$’s in the low-temperature regime.

Figure 9

The magnetic moment $M(h,\alpha )$ and magnetic susceptibility $\chi (h,\alpha )J$ of the system versus the uniform magnetic field $h$ for different values of $\alpha$ at $T=0$.

Figure 10

The magnetic moment $M_z(h,\alpha )$ of the system versus the uniform magnetic field $h$ (in units of $J^{\prime }$, instead of $J$) for $\alpha ⩾{\alpha }_c$ at $T=0$. In the figure, $h_{\mathrm{s}}$ is the saturation field, and $h_{\mathrm{cusp}}$ is the field at the cusp.