Finite low-temperature entropy of some strongly frustrated quantum spin lattices in the vicinity of the saturation field

For a class of highly frustrated antiferromagnetic quantum spin lattices the ground state exhibits a huge degeneracy in high magnetic fields due to the existence of localized magnon states. For some of these spin lattices (in particular, the 1D dimer-plaquette, sawtooth and kagomélike chains as well as the 2D kagomé lattice) we calculate rigorously the ground-state entropy at the saturation field. We find that the ground-state entropy per site remains finite at saturation. This residual ground-state entropy produces a maximum in the field dependence of the isothermal entropy at low temperatures. By numerical calculation of the field dependence of the low-temperature entropy for the sawtooth chain we find that the enhancement of isothermal entropy is robust against small deviations in exchange constants. Moreover, the effect is most pronounced in the extreme quantum case of spin $\frac{1}{2}$.

Figure 1

(Color online) The dimer-plaquette chain which hosts three localized magnons at fat bonds (top) and the auxiliary lattice used for the calculation of the ground-state degeneracy at saturation (bottom). The localized magnons are eigenstates for large enough vertical bonds $J_3⩾J_3^c(J_1,J_2)$ (Ref. 18).

Figure 2

(Color online) The sawtooth chain which hosts three localized magnons at fat $\mathsf{V}$ parts (top) and the auxiliary lattice used for the calculation of the ground-state degeneracy at saturation (bottom). The localized magnons are eigenstates for $J_2=\sqrt{2(1+\Delta )}{J}_1$ (Refs. 4, 5).

Figure 3

(Color online) The kagomélike chain of Ref. 21 which hosts three localized magnons (marked by bold diamonds) and the auxiliary lattice used for the calculation of the ground-state degeneracy at saturation. The localized magnons are eigenstates for exchange bonds of uniform strength (Ref. 4).

Figure 4

(Color online) The kagomélike chain of Refs. 21, 22 which hosts two localized magnons (marked by bold hexagons) and the auxiliary lattice used for the calculation of the ground-state degeneracy at saturation. The localized magnons are eigenstates for $J_2=(1+2\Delta )∕(1+\Delta )J_1$ (Ref. 4).

Figure 5

(Color online) The kagomé lattice which hosts three localized magnons (bold hexagons) and the auxiliary triangular lattice with hard hexagons used for the calculation of the ground-state degeneracy at saturation. The localized magnons are eigenstates for exchange bonds of uniform strength (Ref. 4).

Figure 6

(Color online) The checkerboard lattice which hosts three localized magnons (bold squares) and the auxiliary square lattice with hard squares used for the estimation of the ground-state degeneracy at saturation. The localized magnons are eigenstates for exchange bonds of uniform strength (Ref. 5).

Figure 7

Field dependence of the isothermal entropy per site at low temperatures (upper panel) and higher temperatures (lower panel) for the sawtooth chains of different length $(s=\frac{1}{2},\Delta =1,J_1=1,J_2=2)$.

Figure 8

Field dependence of the isothermal entropy per site of the sawtooth chain at very low temperature (upper panel) and at higher (but still low) temperature (lower panel) as $J_2$ deviates from $\sqrt{2(1+\Delta )}{J}_1$. The corresponding dependence for a linear chain (LC, dotted curves) is also reported for comparison.