The slq(2)-quantum group invariant spin 1/2 XXZ-Heisenberg model with open boundary conditions is investigated by means of the Bethe ansatz. As is well known, quantum groups for q equal to a root of unity possess a finite number of “good” representations with non-zero q-dimension and “bad” ones with vanishing q-dimension. Correspondingly, the state space of an invariant Heisenberg chain decompo...

The general form of the operators commuting with the ground representation (appearing in many physical problems within single particle approximation) of the group is found. With help of the modified group projector technique, this result is applied to the system of identical particles with spin independent interaction, to derive the Dirac-Heisenberg hamiltonian and its effective space for arbit...

that for critical (gapless) quantum system (for the XXZ model when ∆ belongs to the interval (−1, 1)) the entanglement entropy of a block of n spins diverges logarithmically as γ log2 n, while for non critical systems (∆ outside the above mentioned interval), it converges to a constant finite value [1, 2, 3]. This property was interpreted in the framework of conformal field theory [4] associate...

The relevance of zero-energy functions, coming from zero-energy modes and present in the structure of bosonic Green's functions, is often underestimated. Usually, their values are fixed by assuming the ergodicity of the dynamics, but it can be shown that this is not always correct. As the zero-energy functions are connected to fundamental response properties of the system under analysis (specif...

Various series expansions have been developed for the two-layer, S = 1 2 , square lattice Heisenberg antiferromagnet. High temperature expansions are used to calculate the temperature dependence of the susceptibility and specific heat. At T = 0, Ising expansions are used to study the properties of the Néel-ordered phase, while dimer expansions are used to calculate the ground-state properties a...

We study several statistical mechanical models on a general tree. Particular attention is devoted to the classical Heisenberg models, where the state space is the d–dimensional unit sphere and the interactions are proportional to the cosines of the angles between neighboring spins. The phenomenon of interest here is the classification of phase transition (non-uniqueness of the Gibbs state) acco...

The si= 1 2 nearest-neighbor antiferromagnetic Heisenberg model is considered for spins sitting on the vertices of clusters with the connectivity of fullerene molecules and a number of sites n ranging from 24 to 32. Using the permutational and spin-inversion symmetries of the Hamiltonian, the low-energy spectrum is calculated for all the irreducible representations of the symmetry group of each...

In this paper we discuss the construction and the dynamics of vortex-like topological spin excitations in the Schwinger-boson description of Heisenberg antiferromagnets in two dimensions. The topological spin excitations are Dirac fermions (with gap) when spin value S is a half-integer. Experimental and theoretical implications of these excitations are being investigated. 71.10.Fd,75.10.Jm,75.4...

The classical uniaxially anisotropic Heisenberg antiferromagnet on the simple cubic lattice, in the presence of an external magnetic field, is believed to have a multicritical point; however, there has been controversy whether it is a bicritical or a tetracritical point. We perform Monte Carlo simulations of this model and analyze the components of the staggered magnetization, the susceptibilit...

Superconductors with low superfluid density are often dominated by phase fluctuations of the order parameter. In this regime, their physics may be described by XY models. The transition temperature Tc of such models is of the same order as the zero-temperature phase stiffness helicity modulus , a long-wavelength property of the system: Tc=A 0 . However, the constant A is a nonuniversal number, ...