Quantum Heisenberg antiferromagnet in a field on the Tasaki square lattice

Abstract

We consider the $S=1/2$ Heisenberg antiferromagnet on the Tasaki square lattice (flat-band spin system) and study its low-temperature thermodynamics around the saturation magnetic field. To this end, we construct a mapping of the ground states in the subspaces with total $S^z=N/2,\ldots,N/3$ ($N$ is the number of lattice sites) on the hard squares on an auxiliary square lattice and use classical Monte Carlo simulations to examine the latter classical system. The most prominent feature of the $S=1/2$ Heisenberg antiferromagnet on the Tasaki square lattice is an order-disorder phase transition which occurs at a low temperature just below the saturation magnetic field and belongs to the 2D Ising universality class.