Over the last decade, the interest in the spin-
1/2 Heisenberg antiferromagnet (HAF) on the square kagome (also called shuriken) lattice has been growing as a model system of quantum magnetism with a quantum paramagnetic ground state, flat-band physics near the saturation field, and quantum scars. A further motivation to study this model comes from the recent discovery of a gapless spin liquid in the square kagome magnet
KCu6AlBiO4(SO4)5Cl [M. Fujihala et al., Nat. Commun. 11, 3429 (2020)]. Here, we present large-scale numerical investigations of the specific heat
C(T), the entropy
S(T), as well as the susceptibility $\ensuremath{\chi}(T)$ by means of the finite-temperature Lanczos method for system sizes of
N=18,24,30,36,42,48, and
N=54. We find that the specific heat exhibits a low-temperature shoulder below the major maximum which can be attributed to low-lying singlet excitations filling the singlet-triplet gap, which is significantly larger than the singlet-singlet gap. This observation is further supported by the behavior of the entropy
S(T), where a change in curvature is present just at about
T/J=0.2, the same temperature where the shoulder in
C sets in. For the susceptibility the low-lying singlet excitations are irrelevant, and the singlet-triplet gap leads to an exponentially activated low-temperature behavior. The maximum in $\ensuremath{\chi}(T)$ is found at a pretty low temperature
Tmax/J=0.146 (for
N=42) compared to
Tmax/J=0.935 for the unfrustrated square-lattice HAF signaling the crucial role of frustration also for the susceptibility. We find a striking similarity of our square kagome data with the corresponding ones for the kagome HAF down to very low
T. The magnetization process featuring plateaus and jumps and the field dependence of the specific heat that exhibits characteristic peculiarities attributed to the existence of a flat one-magnon band are discussed as well.
The authors investigate the properties of the two-dimensional quantum S=1/2 Heisenberg antiferromagnetic model on a square lattice by means of a block approach. The lattice is divided into four spin square blocks and the Hamiltonian is expressed in terms of low-energy block states. In the framework of the mean-field theory based on the 'auxiliary-boson' formalism; they show that the spin excitation spectrum contains one singlet mode with the temperature-dependent gap and three degenerate triplet modes. The asymptotic low-temperature spin-spin correlations are proportional to R -3/2 exp(-R(1/ xi 1 +1/ xi 2 )), where xi 1 =exp(A/T), xi 2 =constant and A approximately=0.5J. The uniform susceptibility tends to zero in agreement with numerical results; the energy per site is close to -0.57J. Beyond the meanfield theory the authors find gapless collective excitations analogous to the gapless mode in the neutral Fermi gas with attraction.
In analogy to the quantum dimer model on the square lattice introduced by Rokhsar and Kivelson, we identify the low-energy Hilbert space of the spin-1/2 kagom\'e Heisenberg antiferromagnet with the set of dimerized states (nearest-neighbor singlets) and derive an effective Hamiltonian which describes resonance and includes fluctuations into next-nearest-neighbor singlets. Complete diagonalization of this effective Hamiltonian for systems as large as 36 spins makes possible the study of the low-energy thermodynamics of this quantum antiferromagnet and strongly supports the double peak feature in the heat capacity.