Related papers: Quantum Number Fractionalization in Antiferromagne…
Recently it has been suggested by A. M. Tsvelik that quantum S=1/2 antiferromagnet can be described by the Majorana fermions in an irreducible way and without any constraint. In contrast to this claim we shall show that this representation…
We consider a realization of fractional supersymmetric of quantum mechanics of order $r$, where the Hamiltonian and supercharges involve reflection operators. It is shown that the Hamiltonian has $r$-fold degenerate spectrum and the…
We discuss spin-$\frac12$ Heisenberg antiferromagnet on simple square lattice in magnetic field $H$ using recently proposed bond-operator technique. It is well known that magnetically ordered phases of quantum magnets are well described at…
Starting from a modified version of the the S=1/2 Kagome antiferromagnet to emphasize the role of elementary triangles, an effective Hamiltonian involving spin and chirality variables is derived. A mean-field decoupling that retains the…
Problems of strongly interacting electrons can be greatly simplified by reducing them to effective quantum spin models. The initial step is renormalization of the Hamiltonian into a lower energy subspace. The positive and negative U Hubbard…
It is shown that the 2 X 2 matrix Hamiltonian describing the dynamics of a charged spin 1/2 particle with g-factor 2 moving in an arbitrary, spatially dependent, magnetic field in two spatial dimensions can be written as the anticommuator…
We study the magnetic properties of the Kagome antiferromagnet going from the classical limit to the deep quantum regime of spin 1/2 systems. In all the cases there are special values for the magnetization, 1/3 in particular, in which a…
A new variational technique for investigation of the ground state and correlation functions in 1D quantum magnets is proposed. A spin Hamiltonian is reduced to a fermionic representation by the Jordan-Wigner transformation. The ground state…
Spin excitations in an ordered Heisenberg magnet are magnons--bosons with spin 1. That may change when frustration and quantum fluctuations suppress the order and restore the spin-rotation symmetry. We show that spin excitations in the…
A fractional quantization in a two dimensional space is proposed. The angular momenta of the two dimensional electrons are quantized in fractional numbers by the boundary conditions on a multi-layered Riemann surface. Extended wave…
In these lectures, I review some recent results on the Calogero-Sutherland model and the Haldane Shastry-chain. The list of topics I cover are the following: 1) The Calogero-Sutherland Hamiltonian and fractional statistics. The form factor…
A quantum anti-ferromagnetic spin-1 model is characterised on a 2D lattice with the following requirements: i) The Hamiltonian is made out of nearest neighbour interactions. ii) It is homogeneous, translational and rotational invariant.…
The Hamiltonian of relativistic particles with electric and magnetic dipole moments that interact with an electromagnetic field is determined in the Foldy-Wouthuysen representation. Transition to the semiclassical approximation is carried…
Recently the quantum hamiltonian reduction was done in the case of general $s\ell(2)$ embeddings into Lie algebras and superalgebras. In this paper we extend the results to the quantum hamiltonian reduction of $N=1$ affine Lie superalgebras…
Unlike ferromagnetism, antiferromagnetism cannot readily be included in the quasiclassical Keldysh theory because of the rapid spatial variation in the directions of the magnetic moments. The quasiclassical framework is useful because it…
This is an introduction to the microscopic theories of the FQHE. After a brief description of experiments, trial wavefunctions and the physics they contain are discussed. This is followed by a description of the hamiltonian approach,…
The properties of the groundstate and first excitations of 2dimensionnal quantum antiferromagnets are rapidly sketched. A special emphasis is put on the gapped phases: Valence Bond Crystals and the two types of Spin Liquids. New results on…
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions.…
We consider the spin-1/2 antiferromagnetic Heisenberg model on the two-dimensional square-kagome lattice with almost dispersionless lowest magnon band. For a general exchange coupling geometry we elaborate low-energy effective Hamiltonians…
General quantum-mechanical description of relativistic particles and nuclei with spin 1/2 channeled in bent crystals is performed with the use of the cylindrical coordinate system. The previously derived Dirac equation in this system is…