Heisenberg model

One of the most basic models that describes the spin degrees of freedom in solid, which is a reasonable description of many materials in low-energy (low-temperature) scale. There are many variants according to the types and ranges of the interactions, and lattice structures. In particular, the antiferromagnetic Heisenberg model can be obtained from the half-filled Hubbard model through the perturbation with respect to the hopping constant, which makes the model relevant in the study of high-temperature cuprate superconductivity. The case where frustration exists, as in the case of the antiferromagnetic model on a kagome lattice, is a target of active research with the expectation of novel quantum states. The cases without frustration can be studied by quantum Monte Carlo and software packages such as ALPS and DSQSS are available whereas more general cases can be dealt with by exact diagonalization using for exacmple TITPACK, SpinPack, KobePack, and Hphi. Variational Monte Carlo is also an option in the latter case, for which mVMC is available.