Related papers: Introduction to supersymmetric spin networks
We perform a quantization of the loop gravity phase space purely in terms of spinorial variables, which have recently been shown to provide a direct link between spin network states and simplicial geometries. The natural Hilbert space to…
We obtain explicit formulas for the spinor representation $\rho$ of the real orthosymplectic supergroup $\mathrm{OSp}(2p|2q,\mathbb{R})$ by integral 'Gauss--Berezin' operators. Next, we extend $\rho$ to a complex domain and get a…
The isotropic limit of spin systems with orbital degeneracy is shown to have global SU(4) symmetry. On many 2D lattices, the ground state does not posses long range order, which may explain the observed spin liquid properties of $LiNiO_2$.…
We report on the new approach to constructing superconformal extensions of the Calogero-type systems with an arbitrary number of involved particles. It is based upon the superfield gauging of non-abelian isometries of some supersymmetric…
We report on a recent progress in constructing off-shell ${\cal N}=2, 4D$ supersymmetric integer higher-spin theory in terms of unconstrained harmonic analytic gauge superfields and their cubic interaction with the matter hypermultiplets.…
Symmetry plays a fundamental role in physics. The quasi-degeneracy between single-particle orbitals $(n, l, j = l + 1/2)$ and $(n-1, l + 2, j = l + 3/2)$ indicates a hidden symmetry in atomic nuclei, the so-called pseudospin symmetry (PSS).…
We define the notion of a Killing (super)algebra for a connection on a spinor bundle associated to a generalised spin structure on a pseudo-Riemannian manifold of any signature. We are led naturally to include in the even subspace not only…
We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin…
We present a theory of conducting quantum networks that accounts for Abelian and non-Abelian fields acting on spin carriers. We apply this approach to model the conductance of mesoscopic spin interferometers of different geometry (such as…
Spin network systems can be used to achieve quantum state transfer with high fidelity and to generate entanglement. A new approach to design spin-chain-based spin network systems, for shortrange quantum information processing and…
A number of interesting features of the ground states of quantum spin chains are analized with the help of a functional integral representation of the system's equilibrium states. Methods of general applicability are introduced in the…
Superparticle models with $OSp(N|2)$ supersymmetry group are studied. We first consider the $N=4$ case and construct the models with $\kappa$-symmetry on the coset spaces of the $OSp(4|2)$ supergroup. In addition, within the canonical…
The Heisenberg model, a quantum mechanical analogue of the Ising model, has a large ground state degeneracy, due to the symmetry generated by the total spin. This symmetry is also responsible for degeneracies in the rest of the spectrum. We…
We find solutions of the Yang-Baxter equation acting on tensor product of arbitrary representations of the superalgebra sl(2|1). Based on these solutions we construct the local Hamiltonians for integrable homogeneous periodic chains and…
We study a set of exactly soluble spin models in one and two dimensions for any spin $S$. Its ground state, the excitation spectrum, quantum phase transition points, as well as dimensional crossover are determined.
Non-orthogonal bases of projectors on coherent states are introduced to expand hermitean operators acting on the Hilbert space of a spin s. It is shown that the expectation values of a hermitean operator A in a family of (2s+1)(2s+1)…
A superspace formulation is proposed for the osp(1,2)-covariant Lagrangian quantization of general massive gauge theories. The superalgebra os0(1,2) is considered as subalgebra of sl(1,2); the latter may be considered as the algebra of…
We present a detailed study of the gap symmetry and the quasiparticle wave function topology in two-dimensional superconductors without inversion center. The strong spin-orbit coupling of electrons with the crystal lattice makes it…
A strongly correlated electron system associated with the quantum superalgebra ${U}_q[{osp}(2|2)]$ is studied in the framework of the quantum inverse scattering method. By solving the graded reflection equation, two classes of…
We show that the Hilbert space of the standard linear harmonic oscillator is a complete orbit of the osp(2,1;2) spectrum-generating superalgebra, and that this is the smallest such algebraic structure. The ubiquitous appearance of the…