Antiferromagnetic Heisenberg model in a uniform external field

Abstract

We present results on the magnetization curves for the antiferromagnetic Heisenberg model in one and two dimensions.

Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions

“…In this reference, a judicious law for the scaling behaviour for the ground state energy based on numerical results obtained by exact diagonalization on small lattices is proposed, and by differentiation, the magnetization in the thermodynamic limit and at zero temperature is attained. At a low external magnetic field, both results agree with each other with high accuracy, and, as B increases slightly, the deviations appear, which can be conjectured due to the lack of an exact analytical expression for the 23002-9 The dot line data is the one obtained using the scaling behaviour for T = 0 in the thermodynamic limit [16].…”

“…In figure 4, the magnetization density is displayed as a function of the external magnetic field B for three different square lattices of lattice sizes L = 12, 16 and 24, for values of inverse temperature β = 15 and 20. As a comparison, the numerical results obtained in [16] for the magnetization density in the thermodynamic limit and at zero temperature are also displayed. In this reference, a judicious law for the scaling behaviour for the ground state energy based on numerical results obtained by exact diagonalization on small lattices is proposed, and by differentiation, the magnetization in the thermodynamic limit and at zero temperature is attained.…”

“…In figure 2 the magnetization density is shown as a function of the external magnetic field for four different lattice sizes L = 60, 80, 160 and 240 and for three values of the inverse of the temperature β, 15, 20 and 30. As a comparison, we also include the results obtained in [16], which are based on exact diagonalization on small lattice sizes, guessed scaling relations and on the Bethe ansatz to extract the thermodynamic limit of the magnetization at zero temperature. Both results very accurately agree in the whole range of the external magnetic field 0 < B < 2 which shows that indeed the finite size effects are not really important in one dimension.…”

“…Above this critical value, the ground state becomes ferromagnetic in the thermodynamic limit, while below it, the physics is governed by magnons, and the antiferromagnetic order is preferred by the system. In [16] it was shown that the magnetization curve develops a square root singularity as the magnetic field approaches its critical value B c = 2. Quantum entanglement as well as the concurrence have been widely used to find QPT in quantum systems [20,21].…”

“…In figure 6, the magnetization density as a function of the external magnetic field is plotted for a square lattice with size L = 4 at high temperature values T = 0.5, 1.0, 1.5 and 2.0. As a comparison, the sub-plot shows the results from exact numerical diagonalization obtained in [16] for the same parameter values as the ones used in our simulations. Within a remarkable accuracy, both curves agree with each other, which shows how accurately and trustfully the meron-cluster algorithm works in the whole parameter region considered to perform numerical simulations.…”