Inequalities between ground-state energies of Heisenberg models

The Lieb-Schupp inequality is the inequality between ground state en- ergies of certain antiferromagnetic Heisenberg spin systems. In our paper, the numerical value of energy difference given by Lieb-Schupp inequality has been tested for spin systems in various geometries: chains, ladders and quasi-two-dimensional lattices. It turned out that this energy difference was strongly dependent on the class of the system. The relation between this difference and a fall-off of a correlation function has been empirically found and formulated as a conjecture

Long-range order in the XY model on the honeycomb lattice

Using the reflection positivity method, we provide rigorous proof of the existence of long-range magnetic order for the XY model on the honeycomb lattice for large spins S ≥ 2. This is in contrast with the result obtained using the same method but on the square lattice—which gives a stable long-range order for spins S ≥ 1. We suggest that the difference between these two cases stems from the enhanced quantum spin fluctuations on the honeycomb lattice. Using linear spin-wave theory, we show that the enhanced fluctuations are due to the overall much higher kinetic energy of the spin waves on the honeycomb lattice (with Dirac points) than on the square lattice (with good nesting properties)

Quantum Monte Carlo scheme for frustrated Heisenberg antiferromagnets

When one tries to simulate quantum spin systems by the Monte Carlo method, often the 'minus-sign problem' is encountered. In such a case, an application of probabilistic methods is not possible. In this paper the method has been proposed how to avoid the minus sign problem for certain class of frustrated Heisenberg models. The systems where this method is applicable are, for instance, the pyrochlore lattice and the $J_1-J_2$ Heisenberg model. The method works in singlet sector. It relies on expression of wave functions in dimer (pseudo)basis and writing down the Hamiltonian as a sum over plaquettes. In such a formulation, matrix elements of the exponent of Hamiltonian are positive.Comment: 19 LaTeX pages, 6 figures, 1 tabl

Cumulant ratios and their scaling functions for Ising systems in strip geometries

We calculate the fourth-order cumulant ratio (proposed by Binder) for the two-dimensional Ising model in a strip geometry L x oo. The Density Matrix Renormalization Group method enables us to consider typical open boundary conditions up to L=200. Universal scaling functions of the cumulant ratio are determined for strips with parallel as well as opposing surface fields.Comment: 4 pages, RevTex, one .eps figure; references added, format change