Low-temperature thermodynamics for a flat-band ferromagnet: Rigorous versus numerical results

The repulsive Hubbard model on a sawtooth chain exhibits the lowest single-electron band which is completely dispersionless (flat) for a specific choice of the hopping parameters. We construct exact many-electron ground states for electron fillings up to 1/4. We map the low-energy degrees of freedom of the electron model to a model of classical hard dimers on a chain and, as a result, obtain the ground-state degeneracy as well as closed-form expressions for the low-temperature thermodynamic quantities around a particular value of the chemical potential. We compare our analytical findings with complementary numerical data. Although we consider a specific model, we believe that some of our results such as a low-temperature peak in the specific heat are generic for flat-band ferromagnets.

Figure 1

(Color online) (a) Sawtooth lattice with auxiliary lattice for dimer mapping indicated below. Each electron state localized in a valley of the sawtooth lattice corresponds to a dimer on a site of the auxiliary lattice. Closed (open) symbols denote spin-up (spin-down) electrons. The presence of a dimer on a site of the auxiliary lattice excludes the presence of dimers on the two adjacent sites. (b) Main panel: Charge gap $\mathrm{\Delta }\mu =E(N∕2+1)-2E(N∕2)+E(N∕2-1)$ at quarter filling versus $U$. Inset: Hole concentration $n_{\mathrm{h}}∕N=2-n∕N$ versus chemical potential $\mu$ for $U=4t$. (c) Specific heat $C$ per site $N$. Exact diagonalization (ED) results are for $U=4t$. Note that for $\mu =2.04t$ different system sizes are indistinguishable.